Internal problem ID [2770]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 1
Problem number: 15.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {y^{\prime }-x \csc \relax (x )+\cot \relax (x ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 16
dsolve(diff(y(x),x) = x*csc(x)-y(x)*cot(x),y(x), singsol=all)
\[ y \relax (x ) = \frac {\frac {x^{2}}{2}+c_{1}}{\sin \relax (x )} \]
✓ Solution by Mathematica
Time used: 0.041 (sec). Leaf size: 19
DSolve[y'[x]==x*Csc[x]-y[x]*Cot[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} \left (x^2+2 c_1\right ) \csc (x) \\ \end{align*}