\[ y(x) \left (a (\nu -1) x^{2 \nu }+b x^{3 \nu }+\nu ^2-1\right )+x \left (a x^{2 \nu }-\nu ^2+1\right ) y'(x)+x^3 y^{(3)}(x)=0 \] ✓ Mathematica : cpu = 0.0339249 (sec), leaf count = 102
\[\left \{\left \{y(x)\to c_1 x^{1-\nu } e^{\frac {x^{\nu } \text {Root}\left [\text {$\#$1}^3+\text {$\#$1} a+b\& ,1\right ]}{\nu }}+c_2 x^{1-\nu } e^{\frac {x^{\nu } \text {Root}\left [\text {$\#$1}^3+\text {$\#$1} a+b\& ,2\right ]}{\nu }}+c_3 x^{1-\nu } e^{\frac {x^{\nu } \text {Root}\left [\text {$\#$1}^3+\text {$\#$1} a+b\& ,3\right ]}{\nu }}\right \}\right \}\] ✗ Maple : cpu = 0. (sec), leaf count = 0
, result contains DESol or ODESolStruc
\[y \relax (x ) = \mathit {DESol}\left (\left \{x^{3} \left (\frac {d^{3}}{d x^{3}}\textit {\_Y} \relax (x )\right )+\left (x^{2 \nu } a x -\nu ^{2} x +x \right ) \left (\frac {d}{d x}\textit {\_Y} \relax (x )\right )+\left (x^{2 \nu } a \nu -a \,x^{2 \nu }+b \,x^{3 \nu }+\nu ^{2}-1\right ) \textit {\_Y} \relax (x )\right \}, \left \{\textit {\_Y} \relax (x )\right \}\right )\]