\[ x y(x) \left (a y'(x)+b y''(x)+c y^{(3)}(x)+e y^{(4)}(x)\right )=0 \] ✓ Mathematica : cpu = 0.242699 (sec), leaf count = 214
\[\left \{\{y(x)\to 0\},\left \{y(x)\to \frac {c_1 e^{x \text {Root}\left [\text {$\#$1}^3+\frac {\text {$\#$1}^2 c}{e}+\frac {\text {$\#$1} b}{e}+\frac {a}{e}\& ,1\right ]}}{\text {Root}\left [\text {$\#$1}^3+\frac {\text {$\#$1}^2 c}{e}+\frac {\text {$\#$1} b}{e}+\frac {a}{e}\& ,1\right ]}+\frac {c_2 e^{x \text {Root}\left [\text {$\#$1}^3+\frac {\text {$\#$1}^2 c}{e}+\frac {\text {$\#$1} b}{e}+\frac {a}{e}\& ,2\right ]}}{\text {Root}\left [\text {$\#$1}^3+\frac {\text {$\#$1}^2 c}{e}+\frac {\text {$\#$1} b}{e}+\frac {a}{e}\& ,2\right ]}+\frac {c_3 e^{x \text {Root}\left [\text {$\#$1}^3+\frac {\text {$\#$1}^2 c}{e}+\frac {\text {$\#$1} b}{e}+\frac {a}{e}\& ,3\right ]}}{\text {Root}\left [\text {$\#$1}^3+\frac {\text {$\#$1}^2 c}{e}+\frac {\text {$\#$1} b}{e}+\frac {a}{e}\& ,3\right ]}+c_4\right \}\right \}\]
✓ Maple : cpu = 0.039 (sec), leaf count = 679
\[ \left \{ y \left ( x \right ) =0,y \left ( x \right ) ={\it \_C4}\,{{\rm e}^{{\frac {x}{6\,e} \left ( \left ( 12\,\sqrt {3}\sqrt {27\,{a}^{2}{e}^{2}+ \left ( -18\,abc+4\,{b}^{3} \right ) e+4\,a{c}^{3}-{b}^{2}{c}^{2}}e-108\,a{e}^{2}+36\,bce-8\,{c}^{3} \right ) ^{{\frac {2}{3}}}-2\,c\sqrt [3]{12\,\sqrt {3}\sqrt {27\,{a}^{2}{e}^{2}+ \left ( -18\,abc+4\,{b}^{3} \right ) e+4\,a{c}^{3}-{b}^{2}{c}^{2}}e-108\,a{e}^{2}+36\,bce-8\,{c}^{3}}-12\,be+4\,{c}^{2} \right ) {\frac {1}{\sqrt [3]{12\,\sqrt {3}\sqrt {27\,{a}^{2}{e}^{2}+ \left ( -18\,abc+4\,{b}^{3} \right ) e+4\,a{c}^{3}-{b}^{2}{c}^{2}}e-108\,a{e}^{2}+36\,bce-8\,{c}^{3}}}}}}}+{\it \_C3}\,{{\rm e}^{{\frac {x}{12\,e} \left ( \left ( i \left ( 12\,\sqrt {3}\sqrt {27\,{a}^{2}{e}^{2}+ \left ( -18\,abc+4\,{b}^{3} \right ) e+4\,a{c}^{3}-{b}^{2}{c}^{2}}e-108\,a{e}^{2}+36\,bce-8\,{c}^{3} \right ) ^{{\frac {2}{3}}}+12\,ibe-4\,i{c}^{2} \right ) \sqrt {3}+12\,be- \left ( \sqrt [3]{12\,\sqrt {3}\sqrt {27\,{a}^{2}{e}^{2}+ \left ( -18\,abc+4\,{b}^{3} \right ) e+4\,a{c}^{3}-{b}^{2}{c}^{2}}e-108\,a{e}^{2}+36\,bce-8\,{c}^{3}}+2\,c \right ) ^{2} \right ) {\frac {1}{\sqrt [3]{12\,\sqrt {3}\sqrt {27\,{a}^{2}{e}^{2}+ \left ( -18\,abc+4\,{b}^{3} \right ) e+4\,a{c}^{3}-{b}^{2}{c}^{2}}e-108\,a{e}^{2}+36\,bce-8\,{c}^{3}}}}}}}+{\it \_C2}\,{{\rm e}^{-{\frac {x}{12\,e} \left ( \left ( i \left ( 12\,\sqrt {3}\sqrt {27\,{a}^{2}{e}^{2}+ \left ( -18\,abc+4\,{b}^{3} \right ) e+4\,a{c}^{3}-{b}^{2}{c}^{2}}e-108\,a{e}^{2}+36\,bce-8\,{c}^{3} \right ) ^{{\frac {2}{3}}}+12\,ibe-4\,i{c}^{2} \right ) \sqrt {3}-12\,be+ \left ( \sqrt [3]{12\,\sqrt {3}\sqrt {27\,{a}^{2}{e}^{2}+ \left ( -18\,abc+4\,{b}^{3} \right ) e+4\,a{c}^{3}-{b}^{2}{c}^{2}}e-108\,a{e}^{2}+36\,bce-8\,{c}^{3}}+2\,c \right ) ^{2} \right ) {\frac {1}{\sqrt [3]{12\,\sqrt {3}\sqrt {27\,{a}^{2}{e}^{2}+ \left ( -18\,abc+4\,{b}^{3} \right ) e+4\,a{c}^{3}-{b}^{2}{c}^{2}}e-108\,a{e}^{2}+36\,bce-8\,{c}^{3}}}}}}}+{\it \_C1} \right \} \]