Linked Questions

26 votes
5 answers

Accessing Reduce from DSolve

When solving transcendental equations, Solve frequently warns us that inverse functions are being used so that some solutions may not be found. We also see that <...
Mark McClure's user avatar
  • 32.5k
18 votes
5 answers

DSolve not finding solution I expected

Try to solve the following ODE via DSolve $$ \left\{\begin{aligned} y'(x)+2 y(x) e^x-y(x)^2 &= e^{2 x}+e^x \\ y'(0) &=1 \end{aligned}\right. $$ The ...
LCFactorization's user avatar
10 votes
5 answers

NDSolve solves this ordinary differential equation only "half-way"

This system eqs = {(1/2) Y'[x]^2 == (1 - Log[Y[x]^2]) Y[x]^2, Y[0] == 1} is known to have a simple solution in terms of Gaussian functions, which can be checked ...
Konstantin's user avatar
14 votes
4 answers

Does Mathematica evaluate Sqrt[1] to +1 or -1 in this differential equation?

Bug introduced in 8.0 or earlier and persisting through 14.0 or later This is known ode that DSolve generates a wrong extra solution. Been there since 2010. I do ...
Nasser's user avatar
  • 147k
6 votes
3 answers

Nonlinear first order differential equation

I would like to solve: $y - y' x - y'^2 = 0$. One can guess a solution as $y = - x^2 / 4$. However, with Mathematica, I have: ...
user avatar
8 votes
2 answers

Numerical solution to a nonlinear Ordinary Differential Equation

I am trying to solve the following ODE for $f(x)$: $$x f' - f = \frac{(f')^2}{\gamma^2}[1-({f}')^\gamma]^2$$ where $\gamma < 0$ and real, which makes the ODE highly nonlinear. Since I am not ...
Oliver Fabio Piattella's user avatar
9 votes
3 answers

How to find root-free form of an equation

Suppose you have an equation with various roots as in $\sqrt a + \sqrt b = \sqrt c$. Sqrt[a] + Sqrt[b] == Sqrt[c] Is there a Mathematica command or program ...
Maesumi's user avatar
  • 807
5 votes
1 answer

DSolve with Piecewise Function in System of DEQs

I have been messing around with this problem from MSE, which is given by: $$ \ddot{x} = \begin{cases} -x + c\cdot \operatorname{sgn}(x)& |x| > c\\ 0 & |x|\leq c \end{cases} $$ where $c &...
Moo's user avatar
  • 3,388
3 votes
2 answers

Is there any way we can draw its slope field without solving the differential equation?

Some equations are difficult to solve, so perhaps we can plot a function of the equation to see roughly how the solution looks. The same is true for differential equations, where we can observe the ...
yode's user avatar
  • 26.9k
3 votes
2 answers

Why does NDSolve run into problems here?

I am looking at a particle moving in a funny potential, described by the following differential equation. The solution should be just some kind of periodic trajectory, why is there a problem here? ...
korni1990's user avatar
  • 307
11 votes
0 answers

DSolve returns an answer that is not a solution

Investigating DSolve misses a solution of a differential equation, I came across this odd behavior of DSolve. The following DSolve command returns an answer to the ...
Michael E2's user avatar
  • 239k
3 votes
2 answers

Constraint of result of DSolve

I have found the solution of an ODE in Mathematica by the below script: ...
sara nj's user avatar
  • 311
7 votes
2 answers

Question on DSolve's IncludeSingularSolutions option. Why some output do not agree with definition?

in V 13.1, DSolve added a very useful option IncludeSingularSolutions which according to Mathematica own documentation says Singular solutions cannot be obtained ...
Nasser's user avatar
  • 147k
0 votes
3 answers

How to simplify the $Sqrt$ [closed]

I have a expression: 13 + 6 Sqrt[6 - x] x == x I want to simplify the Sqrt to be ...
yode's user avatar
  • 26.9k
2 votes
1 answer

I was wondering why I got the different answer of the same differential equation in two different ways?

Cross-posted in In Mathematica I got the different answer of the same differential equation respectively in analytical method and numerical method. At the ...
dcydhb's user avatar
  • 615
2 votes
0 answers

Stopping NDSolve ahead of a crash

During the evaluation of an NDSolve expression, when it is known that slope goes to infinity at location $y=1$ in the ODE $$\frac{dy}{dx} = \sqrt\frac {y^2+1}{y^2-...
Narasimham's user avatar
  • 3,198
0 votes
0 answers

the question about second order differential equations

I have a second order differential equation with two known initial conditions like this: ...
shrocat's user avatar
  • 189