Internal problem ID [1080]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 2, First order equations. Exact equations. Integrating factors. Section 2.6 Page
91
Problem number: 21.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {a \cos \left (x \right ) y-\sin \left (x \right ) y^{2}+\left (b \cos \left (x \right ) y-y x \sin \left (x \right )\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 67
dsolve((a*cos(x)*y(x)-y(x)*sin(x)*y(x))+(b*cos(x)*y(x)-x*sin(x)*y(x))*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = 0 y \left (x \right ) = \left (\int -\frac {a \cos \left (x \right ) {\mathrm e}^{\int -\frac {\sin \left (x \right )}{-\sin \left (x \right ) x +\cos \left (x \right ) b}d x}}{-\sin \left (x \right ) x +\cos \left (x \right ) b}d x +c_{1} \right ) {\mathrm e}^{\int \frac {\sin \left (x \right )}{-\sin \left (x \right ) x +\cos \left (x \right ) b}d x} \end{align*}
✓ Solution by Mathematica
Time used: 3.564 (sec). Leaf size: 106
DSolve[(a*Cos[x]*y[x]-y[x]*Sin[x]*y[x])+(b*Cos[x]*y[x]-x*Sin[x]*y[x])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 0 y(x)\to \exp \left (\int _1^x\frac {\sin (K[1])}{b \cos (K[1])-K[1] \sin (K[1])}dK[1]\right ) \left (\int _1^x-\frac {a \exp \left (-\int _1^{K[2]}\frac {\sin (K[1])}{b \cos (K[1])-K[1] \sin (K[1])}dK[1]\right ) \cos (K[2])}{b \cos (K[2])-K[2] \sin (K[2])}dK[2]+c_1\right ) y(x)\to 0 \end{align*}