ODE
\[ y'(x) y''(x)=x^2 y(x) y'(x)+x y(x)^2 \] ODE Classification
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_poly_yn]]
Book solution method
TO DO
Mathematica ✗
cpu = 54.4173 (sec), leaf count = 0 , could not solve
DSolve[Derivative[1][y][x]*Derivative[2][y][x] == x*y[x]^2 + x^2*y[x]*Derivative[1][y][x], y[x], x]
Maple ✗
cpu = 5.532 (sec), leaf count = 0 , result contains DESol or ODESolStruc
\[[]\]
Mathematica raw input
DSolve[y'[x]*y''[x] == x*y[x]^2 + x^2*y[x]*y'[x],y[x],x]
Mathematica raw output
DSolve[Derivative[1][y][x]*Derivative[2][y][x] == x*y[x]^2 + x^2*y[x]*Derivative[1][y][x], y[x], x]
Maple raw input
dsolve(diff(y(x),x)*diff(diff(y(x),x),x) = x^2*y(x)*diff(y(x),x)+x*y(x)^2, y(x))
Maple raw output
[]