2.572   ODE No. 572

\[ f\left (y'(x)\right ) \left (x y'(x)-y(x)\right )^n+y(x) g\left (y'(x)\right )+x h\left (y'(x)\right )=0 \]

✗ Mathematica : cpu = 0.0563605 (sec), leaf count = 0

DSolve[x*h[Derivative[1][y][x]] + g[Derivative[1][y][x]]*y[x] + f[Derivative[1][y][x]]*(-y[x] + x*Derivative[1][y][x])^n == 0,y[x],x]
 

, could not solve

DSolve[x*h[Derivative[1][y][x]] + g[Derivative[1][y][x]]*y[x] + f[Derivative[1][y][x]]*(-y[x] + x*Derivative[1][y][x])^n == 0, y[x], x]

✗ Maple : cpu = 0. (sec), leaf count = 0

dsolve((x*diff(y(x),x)-y(x))^n*f(diff(y(x),x))+y(x)*g(diff(y(x),x))+x*h(diff(y(x),x))=0,y(x))
 

, could not solve

dsolve((x*diff(y(x),x)-y(x))^n*f(diff(y(x),x))+y(x)*g(diff(y(x),x))+x*h(diff(y(x),x))=0,y(x))