Internal problem ID [7766]
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]
\[ \boxed {x^{n} y^{\prime }-a y^{2}-b \,x^{-2+2 n}=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 60
dsolve(x^n*diff(y(x),x) - a*y(x)^2 - b*x^(2*n-2)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {x^{n -1} \left (n -1-\tan \left (\frac {\sqrt {4 b a -n^{2}+2 n -1}\, \left (-\ln \left (x \right )+c_{1} \right )}{2}\right ) \sqrt {4 b a -n^{2}+2 n -1}\right )}{2 a} \]
✓ Solution by Mathematica
Time used: 0.511 (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*}