Internal problem ID [3765]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 18
Problem number: 513.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _rational, _Bernoulli]
\[ \boxed {x y y^{\prime }-b y^{2}=a \,x^{n}} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 84
dsolve(x*y(x)*diff(y(x),x) = a*x^n+b*y(x)^2,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \frac {\sqrt {-4 \left (b -\frac {n}{2}\right ) \left (-c_{1} \left (b -\frac {n}{2}\right ) x^{2 b}+a \,x^{n}\right )}}{2 b -n} \\ y \left (x \right ) &= -\frac {\sqrt {-4 \left (b -\frac {n}{2}\right ) \left (-c_{1} \left (b -\frac {n}{2}\right ) x^{2 b}+a \,x^{n}\right )}}{2 b -n} \\ \end{align*}
✓ Solution by Mathematica
Time used: 4.461 (sec). Leaf size: 86
DSolve[x y[x] y'[x]==a x^n+b y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {-2 a x^n+c_1 (2 b-n) x^{2 b}}}{\sqrt {2 b-n}} \\ y(x)\to \frac {\sqrt {-2 a x^n+c_1 (2 b-n) x^{2 b}}}{\sqrt {2 b-n}} \\ \end{align*}