Internal problem ID [3327]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 21
Problem number: 585.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact, _rational, [_Abel, 2nd type, class B]]
Solve \begin {gather*} \boxed {x \left (3-2 x^{2} y\right ) y^{\prime }-4 x +3 y-3 x^{2} y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 47
dsolve(x*(3-2*x^2*y(x))*diff(y(x),x) = 4*x-3*y(x)+3*x^2*y(x)^2,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {3+\sqrt {-8 x^{3}+4 c_{1} x +9}}{2 x^{2}} \\ y \relax (x ) = -\frac {-3+\sqrt {-8 x^{3}+4 c_{1} x +9}}{2 x^{2}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.613 (sec). Leaf size: 71
DSolve[x(3-2 x^2 y[x])y'[x]==4 x-3 y[x]+3 x^2 y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {-3 x+\sqrt {x^2 \left (-8 x^3+4 c_1 x+9\right )}}{2 x^3} \\ y(x)\to \frac {3 x+\sqrt {x^2 \left (-8 x^3+4 c_1 x+9\right )}}{2 x^3} \\ \end{align*}