29.7.28 problem 203

Internal problem ID [4803]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 7
Problem number : 203
Date solved : Monday, January 27, 2025 at 09:40:01 AM
CAS classification : [_separable]

\begin{align*} x y^{\prime }&=y-\cot \left (y\right )^{2} \end{align*}

✓ Solution by Maple

Time used: 0.003 (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: 3.298 (sec). Leaf size: 49

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

\[ y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {\cos (2 K[1])-1}{K[1] \cos (2 K[1])+\cos (2 K[1])-K[1]+1}dK[1]\&\right ][\log (x)+c_1] \]