Internal problem ID [1082]
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: 23.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y \left (x \cos \left (x \right )+2 \sin \left (x \right )\right )+x \left (1+y\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 33
dsolve((y(x)*(x*cos(x)+2*sin(x)))+(x*(y(x)+1))*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{-\operatorname {LambertW}\left ({\mathrm e}^{-\sin \left (x \right )-2 \,\operatorname {Si}\left (x \right )-c_{1}}\right )-\sin \left (x \right )-2 \,\operatorname {Si}\left (x \right )-c_{1}} \]
✓ Solution by Mathematica
Time used: 2.59 (sec). Leaf size: 24
DSolve[(y[x]*(x*Cos[x]+2*Sin[x]))+(x*(y[x]+1))*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to W\left (e^{-2 \text {Si}(x)-\sin (x)+c_1}\right ) \\ y(x)\to 0 \\ \end{align*}