Internal problem ID [1150]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 5 linear second order equations. Section 5.6 Reduction or order. Page
253
Problem number: 39 part(b).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _Riccati]
\[ \boxed {y^{\prime }+y^{2}+4 y x=-4 x^{2}-2} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 23
dsolve(diff(y(x),x)+y(x)^2+4*x*y(x)+4*x^2+2=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {-2 c_{1} x +2 x^{2}-1}{c_{1} -x} \]
✓ Solution by Mathematica
Time used: 0.129 (sec). Leaf size: 22
DSolve[y'[x]+y[x]^2+4*x*y[x]+4*x^2+2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -2 x+\frac {1}{x+c_1} \\ y(x)\to -2 x \\ \end{align*}