Internal problem ID [7612]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 31.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-a \,x^{n} \left (y^{2}+1\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.062 (sec). Leaf size: 22
dsolve(diff(y(x),x) - a*x^n*(y(x)^2+1)=0,y(x), singsol=all)
\[ y \relax (x ) = \tan \left (\frac {a \left (c_{1} n +x^{n +1}+c_{1}\right )}{n +1}\right ) \]
✓ Solution by Mathematica
Time used: 0.74 (sec). Leaf size: 35
DSolve[y'[x] - a*x^n*(y[x]^2+1)==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \tan \left (\frac {a x^{n+1}}{n+1}+c_1\right ) \\ y(x)\to -i \\ y(x)\to i \\ \end{align*}