4.44.21 \(x^2 y'''(x)+\left (6-2 x^3\right ) y'(x)+2 x^3 y(x)+\left (6-x^2\right ) x y''(x)=0\)

ODE
\[ x^2 y'''(x)+\left (6-2 x^3\right ) y'(x)+2 x^3 y(x)+\left (6-x^2\right ) x y''(x)=0 \] ODE Classification

[[_3rd_order, _with_linear_symmetries]]

Book solution method
TO DO

Mathematica ✗
cpu = 61.346 (sec), leaf count = 0 , DifferentialRoot result

\[\left \{\left \{y(x)\to \text {DifferentialRoot}\left [\{\unicode {f818},\unicode {f817}\}\unicode {f4a1}\left \{\unicode {f817}^2 \unicode {f818}^{\text {Symbol}[\text {StringJoin}[\text {ConstantArray}[\prime ,3]]]}(\unicode {f817})+\left (6-2 \unicode {f817}^3\right ) \unicode {f818}'(\unicode {f817})+2 \unicode {f817}^3 \unicode {f818}(\unicode {f817})-\left (\unicode {f817}^2-6\right ) \unicode {f817} \unicode {f818}''(\unicode {f817})=0,\unicode {f818}(1)=c_1,\unicode {f818}'(1)=c_2,\unicode {f818}''(1)=c_3\right \}\right ][x]\right \}\right \}\]

Maple ✗
cpu = 0.289 (sec), leaf count = 0 , result contains DESol

\[ \left \{ y \left ( x \right ) ={\it DESol} \left ( \left \{ 2\,{x}^{3}{\it \_Y} \left ( x \right ) + \left ( -2\,{x}^{3}+6 \right ) {\frac {\rm d}{{\rm d}x}}{\it \_Y} \left ( x \right ) + \left ( -{x}^{3}+6\,x \right ) {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}{\it \_Y} \left ( x \right ) +{x}^{2}{\frac {{\rm d}^{3}}{{\rm d}{x}^{3}}}{\it \_Y} \left ( x \right ) \right \} , \left \{ {\it \_Y} \left ( x \right ) \right \} \right ) \right \} \]

Mathematica raw input

DSolve[2*x^3*y[x] + (6 - 2*x^3)*y'[x] + x*(6 - x^2)*y''[x] + x^2*y'''[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> DifferentialRoot[Function[{\[FormalY], \[FormalX]}, {2*\[FormalX]^3*\[
FormalY][\[FormalX]] + (6 - 2*\[FormalX]^3)*Derivative[1][\[FormalY]][\[FormalX]
] - \[FormalX]*(-6 + \[FormalX]^2)*Derivative[2][\[FormalY]][\[FormalX]] + \[For
malX]^2*Derivative[3][\[FormalY]][\[FormalX]] == 0, \[FormalY][1] == C[1], Deriv
ative[1][\[FormalY]][1] == C[2], Derivative[2][\[FormalY]][1] == C[3]}]][x]}}

Maple raw input

dsolve(x^2*diff(diff(diff(y(x),x),x),x)+x*(-x^2+6)*diff(diff(y(x),x),x)+(-2*x^3+6)*diff(y(x),x)+2*x^3*y(x) = 0, y(x),'implicit')

Maple raw output

y(x) = DESol({2*x^3*_Y(x)+(-2*x^3+6)*diff(_Y(x),x)+(-x^3+6*x)*diff(diff(_Y(x),x)
,x)+x^2*diff(diff(diff(_Y(x),x),x),x)},{_Y(x)})