Internal problem ID [3282]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 1
Problem number: 18.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {y^{\prime }-y \cot \left (x \right )=\sin \left (x \right ) {\mathrm e}^{x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 11
dsolve(diff(y(x),x) = exp(x)*sin(x)+y(x)*cot(x),y(x), singsol=all)
\[ y \left (x \right ) = \left ({\mathrm e}^{x}+c_{1} \right ) \sin \left (x \right ) \]
✓ Solution by Mathematica
Time used: 0.082 (sec). Leaf size: 14
DSolve[y'[x]==Exp[x]*Sin[x]+y[x]*Cot[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \left (e^x+c_1\right ) \sin (x) \]