ODE
\[ 2 x^3 y''(x)+x^2 (2 x y(x)+9) y'(x)+x y(x) \left (-2 x^2 y(x)^2+3 x y(x)+12\right )-6=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✗
cpu = 22.4462 (sec), leaf count = 0 , could not solve
DSolve[-6 + x*y[x]*(12 + 3*x*y[x] - 2*x^2*y[x]^2) + x^2*(9 + 2*x*y[x])*Derivative[1][y][x] + 2*x^3*Derivative[2][y][x] == 0, y[x], x]
Maple ✗
cpu = 4.495 (sec), leaf count = 0 , result contains DESol or ODESolStruc
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Mathematica raw input
DSolve[-6 + x*y[x]*(12 + 3*x*y[x] - 2*x^2*y[x]^2) + x^2*(9 + 2*x*y[x])*y'[x] + 2*x^3*y''[x] == 0,y[x],x]
Mathematica raw output
DSolve[-6 + x*y[x]*(12 + 3*x*y[x] - 2*x^2*y[x]^2) + x^2*(9 + 2*x*y[x])*Derivative[1][y][x] + 2*x^3*Derivative[2][y][x] == 0, y[x], x]
Maple raw input
dsolve(2*x^3*diff(diff(y(x),x),x)+x^2*(9+2*x*y(x))*diff(y(x),x)-6+x*y(x)*(12+3*x*y(x)-2*x^2*y(x)^2) = 0, y(x))
Maple raw output
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