Internal problem ID [2950]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 7
Problem number: 202.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime } x -\left (-2 x^{2}+1\right ) \left (\cot ^{2}\relax (y)\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.006 (sec). Leaf size: 45
dsolve(x*diff(y(x),x) = (-2*x^2+1)*cot(y(x))^2,y(x), singsol=all)
\[ \frac {2 x^{2} \cot \left (y \relax (x )\right )-2 \ln \relax (x ) \cot \left (y \relax (x )\right )+\pi \cot \left (y \relax (x )\right )+2 c_{1} \cot \left (y \relax (x )\right )-2 y \relax (x ) \cot \left (y \relax (x )\right )+2}{2 \cot \left (y \relax (x )\right )} = 0 \]
✓ Solution by Mathematica
Time used: 0.543 (sec). Leaf size: 53
DSolve[x y'[x]==(1-2 x^2)Cot[y[x]]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \text {InverseFunction}\left [\frac {1}{2} (\tan (\text {$\#$1})-\text {$\#$1})\&\right ]\left [-\frac {x^2}{2}+\frac {\log (x)}{2}+c_1\right ] \\ y(x)\to -\frac {\pi }{2} \\ y(x)\to \frac {\pi }{2} \\ \end{align*}