Internal problem ID [3010]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 9
Problem number: 262.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _Riccati]
Solve \begin {gather*} \boxed {y^{\prime } x^{2}+a \,x^{2}+b x y+c y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 71
dsolve(x^2*diff(y(x),x)+a*x^2+b*x*y(x)+c*y(x)^2 = 0,y(x), singsol=all)
\[ y \relax (x ) = -\frac {x \left (\sqrt {4 a c -b^{2}-2 b -1}\, \tan \left (\frac {\ln \relax (x ) \sqrt {4 a c -b^{2}-2 b -1}}{2}+\frac {c_{1} \sqrt {4 a c -b^{2}-2 b -1}}{2}\right )+b +1\right )}{2 c} \]
✓ Solution by Mathematica
Time used: 60.136 (sec). Leaf size: 62
DSolve[x^2 y'[x]+a x^2 +b x y[x]+c y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {x \left (-\sqrt {4 a c-(b+1)^2} \tan \left (\frac {1}{2} \sqrt {4 a c-(b+1)^2} (-\log (x)+c_1)\right )+b+1\right )}{2 c} \\ \end{align*}