Internal problem ID [2916]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 6
Problem number: 168.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, _Riccati]
Solve \begin {gather*} \boxed {y^{\prime } x -a \,x^{2 n}-\left (n +b y\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.008 (sec). Leaf size: 38
dsolve(x*diff(y(x),x) = a*x^(2*n)+(n+b*y(x))*y(x),y(x), singsol=all)
\[ y \relax (x ) = \frac {\tan \left (\frac {x^{n} \sqrt {b}\, \sqrt {a}-c_{1} n}{n}\right ) \sqrt {a}\, x^{n}}{\sqrt {b}} \]
✓ Solution by Mathematica
Time used: 0.338 (sec). Leaf size: 139
DSolve[x y'[x]==a x^(2 n)+(n+b y[x])y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\sqrt {a} x^n \left (-\cos \left (\frac {\sqrt {a} \sqrt {b} x^n}{n}\right )+c_1 \sin \left (\frac {\sqrt {a} \sqrt {b} x^n}{n}\right )\right )}{\sqrt {b} \left (\sin \left (\frac {\sqrt {a} \sqrt {b} x^n}{n}\right )+c_1 \cos \left (\frac {\sqrt {a} \sqrt {b} x^n}{n}\right )\right )} \\ y(x)\to \frac {\sqrt {a} x^n \tan \left (\frac {\sqrt {a} \sqrt {b} x^n}{n}\right )}{\sqrt {b}} \\ \end{align*}