Internal problem ID [2773]
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]
Solve \begin {gather*} \boxed {y^{\prime }-{\mathrm e}^{x} \sin \relax (x )-\cot \relax (x ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.001 (sec). Leaf size: 11
dsolve(diff(y(x),x) = exp(x)*sin(x)+y(x)*cot(x),y(x), singsol=all)
\[ y \relax (x ) = \left ({\mathrm e}^{x}+c_{1}\right ) \sin \relax (x ) \]
✓ Solution by Mathematica
Time used: 0.087 (sec). Leaf size: 14
DSolve[y'[x]==Exp[x]*Sin[x]+y[x]*Cot[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \left (e^x+c_1\right ) \sin (x) \\ \end{align*}