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0
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0answers
38 views

Integro differential eq boundary difficulties

I'm trying numericaly solve simple integro-differential equation, but have some problems with boundary conditions. System: ...
0
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2answers
54 views

Integrating ODE's

I have: $$ m\frac{dV_y}{dt}=-k\cdot V_y-mg $$ where, $V_y$ is velocity in the $y$-direction. I have the initial condition Vy[0]=40 Sin[40 Degrees] and ...
-1
votes
0answers
42 views

I want to calculate $I = \int\limits_0^{ + \infty } {\frac{{\ln \left( t \right)}}{{1 + e^{a - t} }}dt} \quad ;a > 0$ [closed]

plaise $ I = \int\limits_0^{ + \infty } {\frac{{\ln \left( t \right)}}{{1 + e^{a - t} }}dt} \quad ;a > 0 $
0
votes
0answers
28 views

How to solve this linear equation? [migrated]

$(\frac{dy}{dx})^2+6\frac{dy}{dx}+4y=x^{2}e^{2x}$ how to solve this. this is linear equation. what type of equation is it? first order?
0
votes
1answer
40 views

Problems with a constant term in an Integrate command

When asking Mathematica to integrate a function with Integrate, I'm getting drastically different results depending on whether I have a proportionality constant ...
1
vote
2answers
112 views

Solving for the limits of an integral

I am trying to get Mathematica to solve for the symmetric limits of an integral of a Square Wave. ...
0
votes
0answers
27 views

Solving Couples Integrations with Product

I have a set of four coupled integrated equations given below. I was wondering how to go about solving them; since using NDSolve doesn't help. $d(d)/dv= \sin[i]*\cos[i]* ...
1
vote
1answer
101 views

Quantum Physics question [closed]

I'm not sure if anyone here would be able to help me. But if you know a more appropriate place where I could ask for help, please let me know. So here's the question: And here's my attempt at ...
-1
votes
1answer
49 views

Center of gravity of a cylinder in 3D space [closed]

am trying to find the center of gravity coordinates of a cylinder(x,y,z coordinates). however,I cannot figure it out using the triple integral method especially when it comes to the integral bounds. ...
0
votes
1answer
101 views

Solving Integro-Differential equations

I need help solving this equation. Is there a built in function that solves this type of equations? DSolve wouldn't work. Updated equation: ...
0
votes
1answer
36 views

Function to Represent Recursive Integral

I'd like to represent the following recursive integral equation to evaluate/graph (for $n\leq3$): $K_{i,n}\left(x\right)=\intop_{x}^{\infty}K_{i,n-1}\left(y\right)dy$ where ...
4
votes
2answers
170 views

When analytical and numerical methods do not agree - Case study with Maximum Likelihoods methods

Here is the probability distribution I am interested in: $$P(q)=C e^{4 n s q} q^{4 n \nu - 1} (1 - q)^{4 n \mu - 1}$$ , where $e$ is the constant of Euler and $C$ is constant so that the whole thing ...
2
votes
1answer
199 views

Approximate $h$ in $F(\theta)=\sin \theta \int_{-L}^{+L}h(z)e^{-ikz\cos \theta} \,dz$

Consider $$F(\theta)=\sin \theta \int_{-L}^{+L}h(z)e^{-ikz\cos \theta} \,dz$$ $$|z|\le L$$ $$0 \le \theta \le \pi$$ By having knowledge of $F(\theta)$, how can one approximate $h(z)$? In ...
1
vote
0answers
106 views

Solving integro-differential equation

I want to solve the following equation y[t] - y[0] + t y'[0] + Integrate[(t - x) x y[x], {x, 0, t}] == 0; But do not know how to actually solve it. Any ...
1
vote
1answer
123 views

Complex Integration

There are some sequential functions: ...
0
votes
1answer
80 views

Get rid of Error Function: How to get rid of sequential appearances of error function?

We have a function as e[t_] :=(E^(-t^2)) Cos[0.1 t] and we must evaluate below integration (However I used the variable x ...
5
votes
1answer
108 views

Solve a differential equation with an integral inside?

I am trying to solve this differential equation in Mathematica: y'[t]+integral from 0 to t of y[x]dx =e^(-t) where y[0]=0. Is this possible?
0
votes
2answers
36 views

Simplify integration result with conditions

Let's say I have integral Integrate[1/(1 + (f^2/B^2)), {f, 0, Infinity}] The result is $$\text{ConditionalExpression}\left[\frac{\pi }{2 ...
0
votes
1answer
83 views

Mathematica answers `Solve[Integrate[f, x] == x^4, f]` wrong [closed]

The input Solve[Integrate[f, x] == x^4, f] ouputs {{f -> x^3}} Why?
4
votes
1answer
238 views

How to solve this Integral equation

D[x[t] - x[t - 1]/(2 E), {t, 3}] + Integrate[E^(-δ)*x[t - δ]/5^t, {δ, 2, 2.5}] == 0 I found solve this problem is hard with Mathematica. I also find a article ...
1
vote
2answers
80 views

Output of NIntegrate depends on MaxRecursion

I have an integral in this form: ...
0
votes
0answers
59 views

Can Mathematica do this integral over $\mathbb{R}^n$?

I have the following function: $$\phi_{k,n,r}: \mathbb{R}^n \rightarrow \mathbb{R}, (x_1,…,x_n)\mapsto (1-r^{n-k}e^{\sum_{i<k}x_i})e^{\sum_{i<j}x_i-x_j}e^{(2-n)\sum_i x_i}$$. Is there any way ...
1
vote
1answer
78 views

symbolic integration of product of hankel function and trignometric function

I want to perform the following integration. my function is : r*cos(r)hankel(0,kr) i want to integrate from 0->pi , and want to get the expression in terms of k. I used this command ...
0
votes
1answer
117 views
4
votes
2answers
144 views

Compute the average distance from the base of a rectangular pyramid to its apex

How can I compute the average distance from the base of a rectangular pyramid to its apex? For example, if the base of the pyramid is 30 feet by 8 feet, and the height of the pyramid is 12 feet, then ...
1
vote
0answers
97 views

PDE with Integral constraint

I am trying to solve the Non-linear Schrodinger equation $-\Delta \psi(r) + \psi(r) - |\psi(r)|^2\psi(r) = 0$ where $r \in \Omega$ In a square domain ($(x,y) \in \Omega$ where $\Omega=[0,1]\times ...
1
vote
1answer
243 views

Solving Fredholm Equation of the first kind [duplicate]

I want to numerically solve Fredholm integral equations of the first kind, equations of the form $$g(t)=\int_a^b K(t,s)f(s)\,\mathrm{d}s$$ where we know the functions $K(t,s)$ and $g(t)$ and seek to ...
2
votes
0answers
217 views

Solve integral equation for upper bound

I need to find the upper bound of an integral knowing the value of the lower bound and the result of the integral. Here is my function: ...
1
vote
1answer
110 views

Is this integral solvable?

I am trying to solve the below mentioned integral. Is it possible to solve this with mathematica. If not, can I get an approximation for this by introducting the variable not to take certain values ? ...
5
votes
3answers
350 views

Different results of a definite integral $\int_0^{\cosh ^{-1}(a)} \frac{1}{\sqrt{a^2 \text{sech}^2(x)-1}}\, dx$

fixed in 10.0.2 Update I have tried like these. I think there is a bug. ...
2
votes
2answers
228 views

Integration of piecewise function

I'm trying to understand why Mathematica is not evaluating a piecewise function, while it's able to evaluate each of the regions separately. This fails: ...
4
votes
2answers
64 views

DSolve results not what expected

I have the following formula: s'[t] == 230.94 Tan[0.914743 - 0.138564 t] When I solve this by hand I get: ...
0
votes
0answers
103 views

Problem solving a Fredholm integral equation

Based on the algorithm by PlatoManiac presented here Integral equation numerical solution with NDSolve I am solving a Fredholm integral equation with the following constants and arguments: ...
1
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0answers
76 views

Long running time

I gave this data as input: ...
0
votes
1answer
104 views

Problem with integral equations

I have solved an integral equation with the following methods: ...
3
votes
1answer
241 views

Fredholm integral equation of the second kind with kernel containing Bessel and Struve functions

I need to solve this Fredholm integral equation of the second kind: f[s]+integrate[f[t] K[s,t],{t,0,1}]=s where ...
1
vote
2answers
76 views

Integral too slow and with conditionals

When I try to solve this integral: $$\int_{-a}^a \frac{x}{\left(x^2+y^2\right)^{3/2}} \, dy$$ it's return ...
0
votes
1answer
86 views

Calculate integral in limit of very large coefficient

How I can calculate following integrals for large values $\alpha$ in Mathematica: $$ I_1 =\int_{0}^{y} \exp\left(\, -\alpha \sqrt{x(1-x)}\,\right)\, {\rm d}x $$ $$ I_2 =\int_{0}^{y} \exp\left(\, ...
1
vote
1answer
105 views

How to solve an operator form of an integral equation by iteration method?

How I can obtain the $n^{th}$ approximation of the following Operator form integral equation? $F(t)=A(t)+\int_0^tds B(s)F(s)$, where $A(t)=\bigg{(}\begin{matrix}t&0\\Cos(t)&1 ...
4
votes
3answers
253 views

How to solve an integral equation by iteration method? [duplicate]

How I can obtain $n^{th}$ approximation of the following equation $f(t)=t+\int_0^tds f(s)$ by iteration method?
0
votes
1answer
71 views

Compute integral symbolically

I want to compute the following integral: ...
-1
votes
3answers
161 views

Computing integral over explicit region [closed]

I need to integrate $f(x,y)=y^2-2x^2y+6x^3-3xy+2y-6x$ over $\{y\geq 2x^2-2, y\leq 3x\}$ Im using Boole in the following way; ...
2
votes
2answers
302 views

Finding Expectation of function of a Log-normal distribution

Say $Y=g(X)$ and $p_X = \frac{e^{-\frac{(\mu -\log (x))^2}{2 \sigma ^2}}}{\sqrt{2 \pi } x \sigma }$ is Log-normal density function: [Wiki] Find E[Y]? Since $E[Y] = \int_0^\infty y f_Y \ dy = ...
2
votes
5answers
697 views

Compute Triple Integral on spherical coords

I need to compute: $\int \int \int z dxdydz$ over the domain: $\{x^2+y^2+z^2\leqslant 16,z\geqslant 0\}$ Im trying to use spherical coords as: $$\int_{0}^{2\pi} \int_{0}^{\frac{\pi}{2}} ...
0
votes
0answers
43 views

NIntegrate Issue: Changing integration limits makes calculation time extremely long

After a long time developing some code in mathematica and finally getting it to work, I have unfortunately encountered an odd problem: When I change the limits of integration (and shift the function ...
-3
votes
1answer
73 views

Finding integral bounds

i have this integral shown below is equal to 1, and i need to find "a" on mathematica, but I'm not sure how. integral (from 0 to a) sqrt((-50.8938 sin(8.4823 t))^2+(4-11.3097 sin(11.3097 t))^2) dt = ...
0
votes
1answer
87 views

How to calculate definite integral when boundary is a limit?

Integrate[Log[x]/(1-x)^2,{x,eta,Infinity}] The conditions are eta>0, and eta->1, how ...
1
vote
1answer
97 views

Write an expression as a full derivative

Is there a command that tells Mathematica to try to write the terms (if possible) of an expression as total derivates? Example: I want to tell mathematica to write ...