Internal problem ID [3076]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 12
Problem number: 328.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {2 y^{\prime } x^{2}+x \cot \relax (x )-1+2 x^{2} y \cot \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 16
dsolve(2*x^2*diff(y(x),x)+x*cot(x)-1+2*x^2*y(x)*cot(x) = 0,y(x), singsol=all)
\[ y \relax (x ) = -\frac {1}{2 x}+\frac {c_{1}}{\sin \relax (x )} \]
✓ Solution by Mathematica
Time used: 0.074 (sec). Leaf size: 18
DSolve[2 x^2 y'[x]+x Cot[x]-1+2 x^2 y[x] Cot[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{2 x}+c_1 \csc (x) \\ \end{align*}