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### 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 <...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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: ...
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### 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 ...
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 ...
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