Internal problem ID [7767]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 187.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _Riccati]
Solve \begin {gather*} \boxed {x^{n} y^{\prime }-a y^{2}-b \,x^{2 n -2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 76
dsolve(x^n*diff(y(x),x) - a*y(x)^2 - b*x^(2*n-2)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {\left (-\tan \left (-\frac {\ln \relax (x ) \sqrt {4 a b -n^{2}+2 n -1}}{2}+\frac {c_{1} \sqrt {4 a b -n^{2}+2 n -1}}{2}\right ) \sqrt {4 a b -n^{2}+2 n -1}+n -1\right ) x^{n -1}}{2 a} \]
✓ Solution by Mathematica
Time used: 0.537 (sec). Leaf size: 166
DSolve[x^n*y'[x]- a*y[x]^2 - b*x^(2*n-2)==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x^{n-1} \left (\frac {2 \sqrt {a} \sqrt {b} c_1 \sqrt {\frac {(n-1)^2}{a b}-4}}{x^{\sqrt {a} \sqrt {b} \sqrt {\frac {(n-1)^2}{a b}-4}}+c_1}-\sqrt {a} \sqrt {b} \sqrt {\frac {(n-1)^2}{a b}-4}+n-1\right )}{2 a} \\ y(x)\to \frac {x^{n-1} \left (\sqrt {a} \sqrt {b} \sqrt {\frac {(n-1)^2}{a b}-4}+n-1\right )}{2 a} \\ \end{align*}