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]
Solve \begin {gather*} \boxed {y^{\prime }+y^{2}+4 y x +4 x^{2}+2=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 24
dsolve(diff(y(x),x)+y(x)^2+4*x*y(x)+4*x^2+2=0,y(x), singsol=all)
\[ y \relax (x ) = -\frac {-2 x^{2}+2 x c_{1}+1}{c_{1}-x} \]
✓ Solution by Mathematica
Time used: 0.126 (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*}