Internal problem ID [7908]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 328.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _rational]
Solve \begin {gather*} \boxed {a \,x^{2} y^{n} y^{\prime }-2 x y^{\prime }+y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.953 (sec). Leaf size: 33
dsolve(a*x^2*y(x)^n*diff(y(x),x)-2*x*diff(y(x),x)+y(x) = 0,y(x), singsol=all)
\[ y \relax (x )^{2 n} \left (y \relax (x )^{n} a x -n -2\right )^{n} x^{-n}-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.352 (sec). Leaf size: 42
DSolve[y[x] - 2*x*y'[x] + a*x^2*y[x]^n*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {n \left (\log (x)-\log \left (-a x y(x)^n+n+2\right )\right )}{n+2}-\frac {2 n \log (y(x))}{n+2}=c_1,y(x)\right ] \]