Internal problem ID [597]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Miscellaneous problems, end of chapter 2. Page 133
Problem number: 30.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, [_Abel, 2nd type, class B]]
Solve \begin {gather*} \boxed {2 y x +3 y^{2}-\left (x^{2}+2 y x \right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.014 (sec). Leaf size: 35
dsolve(2*x*y(x)+3*y(x)^2-(x^2+2*x*y(x))*diff(y(x),x) = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \left (-\frac {1}{2}-\frac {\sqrt {4 x c_{1}+1}}{2}\right ) x \\ y \relax (x ) = \left (-\frac {1}{2}+\frac {\sqrt {4 x c_{1}+1}}{2}\right ) x \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.286 (sec). Leaf size: 61
DSolve[2*x*y[x]+3*y[x]^2-(x^2+2*x*y[x])*y'[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{2} x \left (1+\sqrt {1+4 e^{c_1} x}\right ) \\ y(x)\to \frac {1}{2} x \left (-1+\sqrt {1+4 e^{c_1} x}\right ) \\ y(x)\to 0 \\ y(x)\to -x \\ \end{align*}