Internal problem ID [2766]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 1
Problem number: 11.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {y^{\prime }-\cos \relax (x ) \sin \relax (x )-\cos \relax (x ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 15
dsolve(diff(y(x),x) = cos(x)*sin(x)+y(x)*cos(x),y(x), singsol=all)
\[ y \relax (x ) = -\sin \relax (x )-1+{\mathrm e}^{\sin \relax (x )} c_{1} \]
✓ Solution by Mathematica
Time used: 0.06 (sec). Leaf size: 18
DSolve[y'[x]==Cos[x]*Sin[x]+y[x]*Cos[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sin (x)+c_1 e^{\sin (x)}-1 \\ \end{align*}