Linked Questions

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
  • 146k
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
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
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
  • 26.8k
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
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
  • 146k
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
  • 26.8k
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
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
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
  • 3,346
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
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
  • 238k
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

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