4.38.28 \(x^3 \left (y''(x)+y(x) y'(x)-y(x)^3\right )+12 x y(x)+24=0\)

ODE
\[ x^3 \left (y''(x)+y(x) y'(x)-y(x)^3\right )+12 x y(x)+24=0 \] ODE Classification

[[_2nd_order, _with_linear_symmetries]]

Book solution method
TO DO

Mathematica ✓
cpu = 22.2207 (sec), leaf count = 40

\[\left \{\left \{y(x)\to -\frac {2+x^3 \wp '(x+c_1;0,c_2)}{x-x^3 \wp (x+c_1;0,c_2)}\right \}\right \}\]

Maple ✗
cpu = 3.941 (sec), leaf count = 0 , result contains DESol or ODESolStruc

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Mathematica raw input

DSolve[24 + 12*x*y[x] + x^3*(-y[x]^3 + y[x]*y'[x] + y''[x]) == 0,y[x],x]

Mathematica raw output

{{y[x] -> -((2 + x^3*WeierstrassPPrime[x + C[1], {0, C[2]}])/(x - x^3*Weierstras
sP[x + C[1], {0, C[2]}]))}}

Maple raw input

dsolve(x^3*(diff(diff(y(x),x),x)+y(x)*diff(y(x),x)-y(x)^3)+12*x*y(x)+24 = 0, y(x))

Maple raw output

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