Internal problem ID [3459]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 7
Problem number: 203.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {x y^{\prime }-y+\cot \left (y\right )^{2}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 22
dsolve(x*diff(y(x),x) = y(x)-cot(y(x))^2,y(x), singsol=all)
\[ \ln \left (x \right )+c_{1} +\int _{}^{y \left (x \right )}\frac {1}{\cot \left (\textit {\_a} \right )^{2}-\textit {\_a}}d \textit {\_a} = 0 \]
✓ Solution by Mathematica
Time used: 3.204 (sec). Leaf size: 49
DSolve[x y'[x]==y[x]-x Cot[y[x]]^2/x,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {\cos (2 K[1])-1}{K[1] \cos (2 K[1])+\cos (2 K[1])-K[1]+1}dK[1]\&\right ][\log (x)+c_1] \]