Internal problem ID [15164]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 12. Miscellaneous problems. Exercises page 93
Problem number: 302.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _rational]
\[ \boxed {x^{2} y^{n} y^{\prime }-2 x y^{\prime }+y=0} \]
✓ Solution by Maple
Time used: 0.203 (sec). Leaf size: 32
dsolve(x^2*y(x)^n*diff(y(x),x)=2*x*diff(y(x),x)-y(x),y(x), singsol=all)
\[ y^{2 n} \left (y^{n} x -n -2\right )^{n} x^{-n}-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.18 (sec). Leaf size: 41
DSolve[x^2*y[x]^n*y'[x]==2*x*y'[x]-y[x],y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {n \left (\log (x)-\log \left (-x y(x)^n+n+2\right )\right )}{n+2}-\frac {2 n \log (y(x))}{n+2}=c_1,y(x)\right ] \]