Internal problem ID [3524]
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]
\[ \boxed {x^{2} y^{\prime }-b x y-y^{2} c \,x^{2}=a} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 57
dsolve(x^2*diff(y(x),x) = a+b*x*y(x)+c*x^2*y(x)^2,y(x), singsol=all)
\[ y \left (x \right ) = -\frac {b +1+\tan \left (\frac {\sqrt {4 a c -b^{2}-2 b -1}\, \left (-\ln \left (x \right )+c_{1} \right )}{2}\right ) \sqrt {4 a c -b^{2}-2 b -1}}{2 c x} \]
✓ Solution by Mathematica
Time used: 0.272 (sec). Leaf size: 99
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 {-4 a c+b^2+2 b+1} \left (1-\frac {2 c_1}{x^{\sqrt {-4 a c+b^2+2 b+1}}+c_1}\right )+b+1}{2 c x} y(x)\to -\frac {-\sqrt {-4 a c+b^2+2 b+1}+b+1}{2 c x} \end{align*}