Internal problem ID [3458]
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]
\[ \boxed {x y^{\prime }-\left (-2 x^{2}+1\right ) \cot \left (y\right )^{2}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 45
dsolve(x*diff(y(x),x) = (-2*x^2+1)*cot(y(x))^2,y(x), singsol=all)
\[ \frac {2 x^{2} \cot \left (y \left (x \right )\right )+\pi \cot \left (y \left (x \right )\right )-2 \ln \left (x \right ) \cot \left (y \left (x \right )\right )+2 c_{1} \cot \left (y \left (x \right )\right )-2 y \left (x \right ) \cot \left (y \left (x \right )\right )+2}{2 \cot \left (y \left (x \right )\right )} = 0 \]
✓ Solution by Mathematica
Time used: 0.555 (sec). Leaf size: 55
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 {$\#$1})-\arctan (\tan (\text {$\#$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*}