Internal problem ID [1078]
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: 19.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, [_Abel, 2nd type, class C]]
Solve \begin {gather*} \boxed {3 y^{3} x^{2}-y^{2}+y+\left (-y x +2 x \right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 59
dsolve((3*x^2*y(x)^3-y(x)^2+y(x))+(-x*y(x)+2*x)*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {4}{\sqrt {x}\, \sqrt {\frac {48 x^{2}+x c_{1}+4}{x}}+2} \\ y \relax (x ) = -\frac {4}{\sqrt {x}\, \sqrt {\frac {48 x^{2}+x c_{1}+4}{x}}-2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.536 (sec). Leaf size: 78
DSolve[(3*x^2*y[x]^3-y[x]^2+y[x])+(-x*y[x]+2*x)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {2}{1+\sqrt {-\frac {1}{x^2}} x \sqrt {-1-4 x (3 x+c_1)}} \\ y(x)\to \frac {2 x}{x+\frac {\sqrt {-1-4 x (3 x+c_1)}}{\sqrt {-\frac {1}{x^2}}}} \\ y(x)\to 0 \\ \end{align*}