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]
\[ \boxed {y y^{\prime } x -y^{2} b=a \,x^{n}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 98
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 {-\left (2 b -n \right ) \left (-2 x^{2 b} c_{1} b +x^{2 b} c_{1} n +2 a \,x^{n}\right )}}{2 b -n} y \left (x \right ) = -\frac {\sqrt {-\left (2 b -n \right ) \left (-2 x^{2 b} c_{1} b +x^{2 b} c_{1} n +2 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*}