ODE
\[ x y(x) y''(x)=a y(x) y'(x)+x y'(x)^2+x y(x)^3 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✗
cpu = 49.0604 (sec), leaf count = 0 , could not solve
DSolve[x*y[x]*Derivative[2][y][x] == x*y[x]^3 + a*y[x]*Derivative[1][y][x] + x*Derivative[1][y][x]^2, y[x], x]
Maple ✗
cpu = 2.556 (sec), leaf count = 0 , result contains DESol or ODESolStruc
\[[]\]
Mathematica raw input
DSolve[x*y[x]*y''[x] == x*y[x]^3 + a*y[x]*y'[x] + x*y'[x]^2,y[x],x]
Mathematica raw output
DSolve[x*y[x]*Derivative[2][y][x] == x*y[x]^3 + a*y[x]*Derivative[1][y][x] + x*Derivative[1][y][x]^2, y[x], x]
Maple raw input
dsolve(x*y(x)*diff(diff(y(x),x),x) = x*diff(y(x),x)^2+a*y(x)*diff(y(x),x)+x*y(x)^3, y(x))
Maple raw output
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