Internal problem ID [3290]
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]]
Solve \begin {gather*} \boxed {\left (3-x +2 y x \right ) y^{\prime }+3 x^{2}-y+y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (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 \relax (x ) = \frac {x -3+\sqrt {-4 x^{4}-4 c_{1} x +x^{2}-6 x +9}}{2 x} \\ y \relax (x ) = -\frac {-x +3+\sqrt {-4 x^{4}-4 c_{1} x +x^{2}-6 x +9}}{2 x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.469 (sec). Leaf size: 71
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 {9+x \left (-4 x^3+x-6+4 c_1\right )}+x-3}{2 x} \\ y(x)\to \frac {\sqrt {9+x \left (-4 x^3+x-6+4 c_1\right )}+x-3}{2 x} \\ \end{align*}