Internal problem ID [3013]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 9
Problem number: 265.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, _Riccati]
Solve \begin {gather*} \boxed {y^{\prime } x^{2}+2+a x \left (-y x +1\right )-x^{2} y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 61
dsolve(x^2*diff(y(x),x)+2+a*x*(1-x*y(x))-x^2*y(x)^2 = 0,y(x), singsol=all)
\[ y \relax (x ) = -\frac {\left (a^{3} x^{3}-a^{2} x^{2}+2 a x -2\right ) {\mathrm e}^{a x}-c_{1}}{x \left (\left (a^{2} x^{2}-2 a x +2\right ) {\mathrm e}^{a x}+c_{1}\right )} \]
✓ Solution by Mathematica
Time used: 0.322 (sec). Leaf size: 68
DSolve[x^2 y'[x]+2+a x(1-x y[x])-x^2 y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {-e^{a x} (a x-1) \left (a^2 x^2+2\right )+a^3 c_1}{x e^{a x} (a x (a x-2)+2)+a^3 c_1 x} \\ y(x)\to \frac {1}{x} \\ \end{align*}