Internal problem ID [3521]
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]
\[ \boxed {y^{\prime } x^{2}+a x \left (-y x +1\right )-y^{2} x^{2}=-2} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 52
dsolve(x^2*diff(y(x),x)+2+a*x*(1-x*y(x))-x^2*y(x)^2 = 0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {-\left (a x -1\right ) \left (x^{2} a^{2}+2\right ) {\mathrm e}^{a x}+c_{1}}{x \left (\left (x^{2} a^{2}-2 a x +2\right ) {\mathrm e}^{a x}+c_{1} \right )} \]
✓ Solution by Mathematica
Time used: 0.366 (sec). Leaf size: 78
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} \left (-a^3 x^3+a^2 x^2-2 a x+2\right )+a^3 c_1}{x \left (e^{a x} \left (a^2 x^2-2 a x+2\right )+a^3 c_1\right )} \\ y(x)\to \frac {1}{x} \\ \end{align*}