4.35.21 \(\left (x^3+1\right ) x y''(x)-\left (1-x^3\right ) y'(x)+x^2 (-y(x))=0\)

ODE
\[ \left (x^3+1\right ) x y''(x)-\left (1-x^3\right ) y'(x)+x^2 (-y(x))=0 \] ODE Classification

[[_2nd_order, _with_linear_symmetries]]

Book solution method
TO DO

Mathematica ✓
cpu = 0.303765 (sec), leaf count = 57

\[\left \{\left \{y(x)\to -\frac {1}{2} c_2 \sqrt [3]{x^3+1} x^2 \, _2F_1\left (\frac {1}{3},\frac {2}{3};\frac {5}{3};-x^3\right )+c_1 \sqrt [3]{x^3+1}+c_2 x^2\right \}\right \}\]

Maple ✓
cpu = 0.151 (sec), leaf count = 30

\[ \left \{ y \left ( x \right ) =\sqrt [3]{{x}^{3}+1} \left ( {\mbox {$_2$F$_1$}({\frac {2}{3}},{\frac {4}{3}};\,{\frac {5}{3}};\,-{x}^{3})}{\it \_C1}\,{x}^{2}+{\it \_C2} \right ) \right \} \] Mathematica raw input

DSolve[-(x^2*y[x]) - (1 - x^3)*y'[x] + x*(1 + x^3)*y''[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> (1 + x^3)^(1/3)*C[1] + x^2*C[2] - (x^2*(1 + x^3)^(1/3)*C[2]*Hypergeome
tric2F1[1/3, 2/3, 5/3, -x^3])/2}}

Maple raw input

dsolve(x*(x^3+1)*diff(diff(y(x),x),x)-(-x^3+1)*diff(y(x),x)-x^2*y(x) = 0, y(x),'implicit')

Maple raw output

y(x) = (x^3+1)^(1/3)*(hypergeom([2/3, 4/3],[5/3],-x^3)*_C1*x^2+_C2)