7.28 problem 203

Internal problem ID [2951]

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]

Solve \begin {gather*} \boxed {y^{\prime } x -y+\cot ^{2}\relax (y)=0} \end {gather*}

Solution by Maple

Time used: 0.004 (sec). Leaf size: 26

dsolve(x*diff(y(x),x) = y(x)-cot(y(x))^2,y(x), singsol=all)
 

\[ \ln \relax (x )+c_{1}-\left (\int _{}^{y \relax (x )}-\frac {1}{\cot ^{2}\left (\textit {\_a} \right )-\textit {\_a}}d \textit {\_a} \right ) = 0 \]

Solution by Mathematica

Time used: 2.585 (sec). Leaf size: 49

DSolve[x y'[x]==y[x]-x Cot[y[x]]^2/x,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} 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] \\ \end{align*}