Internal problem ID [7766]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 186.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _Riccati]
Solve \begin {gather*} \boxed {x^{n} y^{\prime }+y^{2}-\left (n -1\right ) x^{n -1} y+x^{2 n -2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.062 (sec). Leaf size: 17
dsolve(x^n*diff(y(x),x) + y(x)^2 -(n-1)*x^(n-1)*y(x) + x^(2*n-2)=0,y(x), singsol=all)
\[ y \relax (x ) = \tan \left (-\ln \relax (x )+c_{1}\right ) x^{n -1} \]
✓ Solution by Mathematica
Time used: 0.647 (sec). Leaf size: 19
DSolve[x^n*y'[x] + y[x]^2 -(n-1)*x^(n-1)*y[x] + x^(2*n-2)==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x^{n-1} \tan (-\log (x)+c_1) \\ \end{align*}