Internal problem ID [3173]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 15
Problem number: 427.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y y^{\prime }-a x -b x y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.006 (sec). Leaf size: 50
dsolve(y(x)*diff(y(x),x) = a*x+b*x*y(x)^2,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {\sqrt {b \left ({\mathrm e}^{b \,x^{2}} c_{1} b -a \right )}}{b} \\ y \relax (x ) = -\frac {\sqrt {b \left ({\mathrm e}^{b \,x^{2}} c_{1} b -a \right )}}{b} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.795 (sec). Leaf size: 98
DSolve[y[x] y'[x]==a x+b x y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {-a+e^{b \left (x^2+2 c_1\right )}}}{\sqrt {b}} \\ y(x)\to \frac {\sqrt {-a+e^{b \left (x^2+2 c_1\right )}}}{\sqrt {b}} \\ y(x)\to -\frac {i \sqrt {a}}{\sqrt {b}} \\ y(x)\to \frac {i \sqrt {a}}{\sqrt {b}} \\ \end{align*}