Internal problem ID [3522]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 9
Problem number: 266.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _rational, [_Riccati, _special]]
\[ \boxed {x^{2} y^{\prime }-b \,x^{2} y^{2}=a} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 40
dsolve(x^2*diff(y(x),x) = a+b*x^2*y(x)^2,y(x), singsol=all)
\[ y \left (x \right ) = -\frac {1+\tan \left (\frac {\sqrt {4 a b -1}\, \left (-\ln \left (x \right )+c_{1} \right )}{2}\right ) \sqrt {4 a b -1}}{2 b x} \]
✓ Solution by Mathematica
Time used: 0.188 (sec). Leaf size: 77
DSolve[x^2 y'[x]==a+b x^2 y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {-1+\sqrt {1-4 a b} \left (-1+\frac {2 c_1}{x^{\sqrt {1-4 a b}}+c_1}\right )}{2 b x} y(x)\to \frac {\sqrt {1-4 a b}-1}{2 b x} \end{align*}