Internal problem ID [3330]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 21
Problem number: 588.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {x y \left (b \,x^{2}+a \right ) y^{\prime }-A -B y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.01 (sec). Leaf size: 82
dsolve(x*y(x)*(b*x^2+a)*diff(y(x),x) = A+B*y(x)^2,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {\sqrt {-B \left (-x^{\frac {2 B}{a}} \left (b \,x^{2}+a \right )^{-\frac {B}{a}} c_{1} B +A \right )}}{B} \\ y \relax (x ) = -\frac {\sqrt {-B \left (-x^{\frac {2 B}{a}} \left (b \,x^{2}+a \right )^{-\frac {B}{a}} c_{1} B +A \right )}}{B} \\ \end{align*}
✓ Solution by Mathematica
Time used: 1.72 (sec). Leaf size: 134
DSolve[x y[x] (a+b x^2)y'[x]==A+B y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {-A+e^{2 B c_1} x^{\frac {2 B}{a}} \left (a+b x^2\right )^{-\frac {B}{a}}}}{\sqrt {B}} \\ y(x)\to \frac {\sqrt {-A+e^{2 B c_1} x^{\frac {2 B}{a}} \left (a+b x^2\right )^{-\frac {B}{a}}}}{\sqrt {B}} \\ y(x)\to -\frac {i \sqrt {A}}{\sqrt {B}} \\ y(x)\to \frac {i \sqrt {A}}{\sqrt {B}} \\ \end{align*}