Internal problem ID [3279]
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]
\[ \boxed {y^{\prime }+y \cot \left (x \right )=x \csc \left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 16
dsolve(diff(y(x),x) = x*csc(x)-y(x)*cot(x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\frac {x^{2}}{2}+c_{1}}{\sin \left (x \right )} \]
✓ Solution by Mathematica
Time used: 0.039 (sec). Leaf size: 19
DSolve[y'[x]==x*Csc[x]-y[x]*Cot[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} \left (x^2+2 c_1\right ) \csc (x) \]