# 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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