Internal problem ID [3016]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 10
Problem number: 268.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _rational, _Riccati]
Solve \begin {gather*} \boxed {y^{\prime } x^{2}-a -b y x -c \,x^{2} y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.007 (sec). Leaf size: 73
dsolve(x^2*diff(y(x),x) = a+b*x*y(x)+c*x^2*y(x)^2,y(x), singsol=all)
\[ y \relax (x ) = -\frac {\tan \left (-\frac {\ln \relax (x ) \sqrt {4 a c -b^{2}-2 b -1}}{2}+\frac {c_{1} \sqrt {4 a c -b^{2}-2 b -1}}{2}\right ) \sqrt {4 a c -b^{2}-2 b -1}+b +1}{2 c x} \]
✓ Solution by Mathematica
Time used: 0.294 (sec). Leaf size: 93
DSolve[x^2 y'[x]==a+b x y[x]+c x^2 y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {(b+1)^2-4 a c} \left (1-\frac {2 c_1}{x^{\sqrt {(b+1)^2-4 a c}}+c_1}\right )+b+1}{2 c x} \\ y(x)\to \frac {\sqrt {(b+1)^2-4 a c}-b-1}{2 c x} \\ \end{align*}