Internal problem ID [3798]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 20
Problem number: 546.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact, _rational, [_Abel, `2nd type`, `class B`]]
\[ \boxed {\left (3-x +2 y x \right ) y^{\prime }-y+y^{2}=-3 x^{2}} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 63
dsolve((3-x+2*x*y(x))*diff(y(x),x)+3*x^2-y(x)+y(x)^2 = 0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = \frac {-3+x +\sqrt {-4 x^{4}-4 c_{1} x +x^{2}-6 x +9}}{2 x} y \left (x \right ) = -\frac {3-x +\sqrt {-4 x^{4}-4 c_{1} x +x^{2}-6 x +9}}{2 x} \end{align*}
✓ Solution by Mathematica
Time used: 0.555 (sec). Leaf size: 75
DSolve[(3-x+2 x y[x])y'[x]+3 x^2-y[x]+y[x]^2==0 ,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {-4 x^4+x^2-6 x+4 c_1 x+9}-x+3}{2 x} y(x)\to \frac {\sqrt {-4 x^4+x^2+(-6+4 c_1) x+9}+x-3}{2 x} \end{align*}