ODE
\[ \left (x^2+2 y(x)^2 y'(x)\right ) y''(x)+2 y(x) y'(x)^3+3 x y'(x)+y(x)=0 \] ODE Classification
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_poly_yn]]
Book solution method
TO DO
Mathematica ✗
cpu = 42.3579 (sec), leaf count = 0 , could not solve
DSolve[y[x] + 3*x*Derivative[1][y][x] + 2*y[x]*Derivative[1][y][x]^3 + (x^2 + 2*y[x]^2*Derivative[1][y][x])*Derivative[2][y][x] == 0, y[x], x]
Maple ✗
cpu = 8.875 (sec), leaf count = 0 , result contains DESol or ODESolStruc
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Mathematica raw input
DSolve[y[x] + 3*x*y'[x] + 2*y[x]*y'[x]^3 + (x^2 + 2*y[x]^2*y'[x])*y''[x] == 0,y[x],x]
Mathematica raw output
DSolve[y[x] + 3*x*Derivative[1][y][x] + 2*y[x]*Derivative[1][y][x]^3 + (x^2 + 2*y[x]^2*Derivative[1][y][x])*Derivative[2][y][x] == 0, y[x], x]
Maple raw input
dsolve((x^2+2*y(x)^2*diff(y(x),x))*diff(diff(y(x),x),x)+2*y(x)*diff(y(x),x)^3+3*x*diff(y(x),x)+y(x) = 0, y(x))
Maple raw output
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