Internal problem ID [3518]
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]
\[ \boxed {x^{2} y^{\prime }+b x y+c y^{2}=-a \,x^{2}} \]
✓ Solution by Maple
Time used: 0.016 (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)
\[ y \left (x \right ) = -\frac {x \left (\sqrt {4 a c -b^{2}-2 b -1}\, \tan \left (\frac {\ln \left (x \right ) \sqrt {4 a c -b^{2}-2 b -1}}{2}+\frac {c_{1} \sqrt {4 a c -b^{2}-2 b -1}}{2}\right )+b +1\right )}{2 c} \]
✓ Solution by Mathematica
Time used: 60.134 (sec). Leaf size: 66
DSolve[x^2 y'[x]+a x^2 +b x y[x]+c y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {x \left (-\sqrt {4 a c-b^2-2 b-1} \tan \left (\frac {1}{2} \sqrt {4 a c-b^2-2 b-1} (-\log (x)+c_1)\right )+b+1\right )}{2 c} \]