Internal problem ID [7722]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 142.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, _Riccati]
Solve \begin {gather*} \boxed {x^{2} \left (y^{\prime }-y^{2}\right )-a \,x^{2} y+a x +2=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 61
dsolve(x^2*(diff(y(x),x)-y(x)^2) - a*x^2*y(x) + a*x + 2=0,y(x), singsol=all)
\[ y \relax (x ) = -\frac {\left (x^{3} a^{3}-a^{2} x^{2}+2 a x -2\right ) {\mathrm e}^{a x}-c_{1}}{x \left (\left (a^{2} x^{2}-2 a x +2\right ) {\mathrm e}^{a x}+c_{1}\right )} \]
✓ Solution by Mathematica
Time used: 0.552 (sec). Leaf size: 68
DSolve[x^2*(y'[x]-y[x]^2) - a*x^2*y[x] + a*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*}