# Questions tagged [integral-equations]

Questions which deal with or solve for functions expressed in integral form, i.e., one or more unknown functions that appear under an integral sign.

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### Integral (analytic) solving take too long

I'm it my first use mathematica. I need to solved integral in analytical form, this integral: Integrate[1/Sqrt[x^2 + (y - h - t)^2 + z^2], {t, -c, c}] x,y,h,z - some real parameters.
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### integrate second derivative

eq1 = -f1''[x] - (2f1'[x])/x +(f1[x])^3 + f2[x]f1[x] == 0; eq2 = f2''[x] + (2f2'[x])/x - (f1[x])^3 == 0 sol = NDSolve[ {eq1, eq2, f1[1] == 0.1, f2[1] == -0.1,f1'[0.1] == 0.1, f2'[0.1] == 0.1}, {f1, f2}...
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### NDsolve Boundary Condition is a Function of the Solution

I am trying to solve something like Fick's Law using NDSolve: $$\frac{\partial \varphi}{\partial t}=\frac{\partial^2 \varphi}{\partial r^2}+F(r,t)$$ Subject to a ...
308 views
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### Solving the Lotka-McKendrick model with NDSolve

The Lotka-McKendrick model is a demographic model that represents the way a population changes over time due to fertility and mortality. For an age-specific population density $u(a, t)$, and a total ...
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### Getting two different results for the same computation

I have the following two codes: ...
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### How to find the expectation $\mathbb{E}\left[ a \mathcal{Q} \left( \sqrt{b } \gamma \right) \right]$?

I'm trying to find the following expectation $$\mathbb{E}\left[ a \mathcal{Q} \left( \sqrt{b } \gamma \right) \right],$$ where $a$ and $b$ are constant values, $\mathcal{Q}$ is the Gaussian Q-function,...
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### Integral of $r \frac{2^{r-1} \log (2) e^{-\frac{\sqrt{2^r-1}}{b}} \left(2^r-1\right)^{\frac{d}{2}-1}}{b^d \Gamma (d)}$ with Mathematica

I'm trying to find the integral given below with Mathematica $\int_0^{\infty } r \frac{2^{r-1} \log (2) e^{-\frac{\sqrt{2^r-1}}{b}} \left(2^r-1\right)^{\frac{d}{2}-1}}{b^d \Gamma (d)} \, dr$ However, ...
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### Gaussian Integral incorrect

I'm trying to learn about the Gaussian Normal distribution using Mathematica. So I defined my Gaussian like this ...