2.188   ODE No. 188

\[ -a y(x)^3-b n x^3+x^{2 n+1} y'(x)=0 \]

✗ Mathematica : cpu = 12.0681 (sec), leaf count = 0

DSolve[-(b*n*x^3) - a*y[x]^3 + x^(1 + 2*n)*Derivative[1][y][x] == 0,y[x],x]
 

, could not solve

DSolve[-(b*n*x^3) - a*y[x]^3 + x^(1 + 2*n)*Derivative[1][y][x] == 0, y[x], x]

✓ Maple : cpu = 0.046 (sec), leaf count = 32

dsolve(x^(2*n+1)*diff(y(x),x)-a*y(x)^3-b*x^(3*n) = 0,y(x))
 

\[y \left (x \right ) = \operatorname {RootOf}\left (-\ln \left (x \right )+c_{1} +\int _{}^{\textit {\_Z}}\frac {1}{\textit {\_a}^{3} a -n \textit {\_a} +b}d \textit {\_a} \right ) x^{n}\]