Linked Questions

14 votes
4 answers
831 views

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 ...
7 votes
2 answers
125 views

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 ...
18 votes
5 answers
9k views

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 ...
8 votes
2 answers
844 views

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 ...
6 votes
3 answers
695 views

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: ...
3 votes
2 answers
297 views

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 ...
26 votes
5 answers
3k views

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 <...
3 votes
2 answers
223 views

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? ...
0 votes
0 answers
92 views

the question about second order differential equations

I have a second order differential equation with two known initial conditions like this: ...
3 votes
2 answers
296 views

Constraint of result of DSolve

I have found the solution of an ODE in Mathematica by the below script: ...
10 votes
5 answers
2k views

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 ...
9 votes
3 answers
274 views

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 ...
0 votes
3 answers
188 views

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 ...
2 votes
0 answers
216 views

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-...
2 votes
1 answer
611 views

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

Cross-posted in https://www.zhihu.com/question/40784580 In Mathematica I got the different answer of the same differential equation respectively in analytical method and numerical method. At the ...

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