Internal problem ID [1072]
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: 12.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {x^{2} y+4 y x +2 y+\left (x^{2}+x \right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 18
dsolve((x^2*y(x)+4*x*y(x)+2*y(x))+(x^2+x)*diff(y(x),x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} {\mathrm e}^{-x}}{x^{2} \left (x +1\right )} \]
✓ Solution by Mathematica
Time used: 0.043 (sec). Leaf size: 26
DSolve[(x^2*y[x]+4*x*y[x]+2*y[x])+(x^2+x)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {c_1 e^{-x}}{x^2 (x+1)} \\ y(x)\to 0 \\ \end{align*}