Internal problem ID [3086]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 12
Problem number: 338.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _Riccati]
Solve \begin {gather*} \boxed {a \,x^{2} y^{\prime }-x^{2}-a x y-b^{2} y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.006 (sec). Leaf size: 19
dsolve(a*x^2*diff(y(x),x) = x^2+a*x*y(x)+b^2*y(x)^2,y(x), singsol=all)
\[ y \relax (x ) = \frac {\tan \left (\frac {b \left (\ln \relax (x )+c_{1}\right )}{a}\right ) x}{b} \]
✓ Solution by Mathematica
Time used: 0.233 (sec). Leaf size: 22
DSolve[a x^2 y'[x]==x^2+a x y[x]+b^2 y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x \tan \left (b \left (\frac {\log (x)}{a}+c_1\right )\right )}{b} \\ \end{align*}