Internal problem ID [3764]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 18
Problem number: 512.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {x y y^{\prime }-b y^{2}=a} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 48
dsolve(x*y(x)*diff(y(x),x) = a+b*y(x)^2,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \frac {\sqrt {-b \left (-x^{2 b} c_{1} b +a \right )}}{b} \\ y \left (x \right ) &= -\frac {\sqrt {-b \left (-x^{2 b} c_{1} b +a \right )}}{b} \\ \end{align*}
✓ Solution by Mathematica
Time used: 1.6 (sec). Leaf size: 94
DSolve[x y[x] y'[x]==a+b y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {-a+e^{2 b (\log (x)+c_1)}}}{\sqrt {b}} \\ y(x)\to \frac {\sqrt {-a+e^{2 b (\log (x)+c_1)}}}{\sqrt {b}} \\ y(x)\to -\frac {i \sqrt {a}}{\sqrt {b}} \\ y(x)\to \frac {i \sqrt {a}}{\sqrt {b}} \\ \end{align*}