Internal problem ID [2479]
Book: Differential equations, Shepley L. Ross, 1964
Section: 2.4, page 55
Problem number: 1.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, [_Abel, 2nd type, class B]]
Solve \begin {gather*} \boxed {5 y x +4 y^{2}+1+\left (x^{2}+2 y x \right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.007 (sec). Leaf size: 59
dsolve((5*x*y(x)+4*y(x)^2+1)+(x^2+2*x*y(x))*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {-x^{3}-\sqrt {x^{6}-x^{4}-4 c_{1}}}{2 x^{2}} \\ y \relax (x ) = \frac {-x^{3}+\sqrt {x^{6}-x^{4}-4 c_{1}}}{2 x^{2}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.432 (sec). Leaf size: 84
DSolve[(5*x*y[x]+4*y[x]^2+1)+(x^2+2*x*y[x])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {x^5+\sqrt {x^3} \sqrt {x^7-x^5+4 c_1 x}}{2 x^4} \\ y(x)\to -\frac {x}{2}+\frac {\sqrt {x^3} \sqrt {x^7-x^5+4 c_1 x}}{2 x^4} \\ \end{align*}