29.12.9 problem 328

Internal problem ID [4928]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 12
Problem number : 328
Date solved : Monday, January 27, 2025 at 09:51:35 AM
CAS classification : [_linear]

\begin{align*} 2 x^{2} y^{\prime }+x \cot \left (x \right )-1+2 x^{2} y \cot \left (x \right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 14

dsolve(2*x^2*diff(y(x),x)+x*cot(x)-1+2*x^2*y(x)*cot(x) = 0,y(x), singsol=all)
 

\[ y \left (x \right ) = -\frac {1}{2 x}+\csc \left (x \right ) c_{1} \]

✓ Solution by Mathematica

Time used: 0.059 (sec). Leaf size: 18

DSolve[2 x^2 D[y[x],x]+x Cot[x]-1+2 x^2 y[x] Cot[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {1}{2 x}+c_1 \csc (x) \]