ODE
\[ \left (2 x^2 y'(x)+y(x)^2\right ) y''(x)+2 (y(x)+x) y'(x)^2+x y'(x)+y(x)=0 \] ODE Classification
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_poly_yn]]
Book solution method
TO DO
Mathematica ✗
cpu = 42.2317 (sec), leaf count = 0 , could not solve
DSolve[y[x] + x*Derivative[1][y][x] + 2*(x + y[x])*Derivative[1][y][x]^2 + (y[x]^2 + 2*x^2*Derivative[1][y][x])*Derivative[2][y][x] == 0, y[x], x]
Maple ✗
cpu = 6.881 (sec), leaf count = 0 , result contains DESol or ODESolStruc
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Mathematica raw input
DSolve[y[x] + x*y'[x] + 2*(x + y[x])*y'[x]^2 + (y[x]^2 + 2*x^2*y'[x])*y''[x] == 0,y[x],x]
Mathematica raw output
DSolve[y[x] + x*Derivative[1][y][x] + 2*(x + y[x])*Derivative[1][y][x]^2 + (y[x]^2 + 2*x^2*Derivative[1][y][x])*Derivative[2][y][x] == 0, y[x], x]
Maple raw input
dsolve((y(x)^2+2*x^2*diff(y(x),x))*diff(diff(y(x),x),x)+2*(x+y(x))*diff(y(x),x)^2+x*diff(y(x),x)+y(x) = 0, y(x))
Maple raw output
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