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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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### 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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### 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: ...
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 ...
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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 ...
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### 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 ...
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300 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 ...
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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? ...
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296 views

### Constraint of result of DSolve

I have found the solution of an ODE in Mathematica by the below script: ...
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