Internal problem ID [3170]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 15
Problem number: 424.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, _Bernoulli]
Solve \begin {gather*} \boxed {y y^{\prime }-a x -b y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 61
dsolve(y(x)*diff(y(x),x) = a*x+b*y(x)^2,y(x), singsol=all)
\begin{align*} y \relax (x ) = -\frac {\sqrt {4 \,{\mathrm e}^{2 b x} c_{1} b^{2}-4 b x a -2 a}}{2 b} \\ y \relax (x ) = \frac {\sqrt {4 \,{\mathrm e}^{2 b x} c_{1} b^{2}-4 b x a -2 a}}{2 b} \\ \end{align*}
✓ Solution by Mathematica
Time used: 9.997 (sec). Leaf size: 77
DSolve[y[x] y'[x]==a x+b y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {i \sqrt {a \left (b x+\frac {1}{2}\right )-b^2 c_1 e^{2 b x}}}{b} \\ y(x)\to \frac {i \sqrt {a \left (b x+\frac {1}{2}\right )-b^2 c_1 e^{2 b x}}}{b} \\ \end{align*}