\[ x y(x) \left (a y'(x)+b y''(x)+c y^{(3)}(x)+e y^{(4)}(x)\right )=0 \] ✓ Mathematica : cpu = 0.148925 (sec), leaf count = 214
DSolve[x*y[x]*(a*Derivative[1][y][x] + b*Derivative[2][y][x] + c*Derivative[3][y][x] + e*Derivative[4][y][x]) == 0,y[x],x]
\[\left \{\{y(x)\to 0\},\left \{y(x)\to \frac {c_1 e^{x \text {Root}\left [\text {$\#$1}^3+\frac {\text {$\#$1}^2 c}{e}+\frac {\text {$\#$1} b}{e}+\frac {a}{e}\& ,1\right ]}}{\text {Root}\left [\text {$\#$1}^3+\frac {\text {$\#$1}^2 c}{e}+\frac {\text {$\#$1} b}{e}+\frac {a}{e}\& ,1\right ]}+\frac {c_2 e^{x \text {Root}\left [\text {$\#$1}^3+\frac {\text {$\#$1}^2 c}{e}+\frac {\text {$\#$1} b}{e}+\frac {a}{e}\& ,2\right ]}}{\text {Root}\left [\text {$\#$1}^3+\frac {\text {$\#$1}^2 c}{e}+\frac {\text {$\#$1} b}{e}+\frac {a}{e}\& ,2\right ]}+\frac {c_3 e^{x \text {Root}\left [\text {$\#$1}^3+\frac {\text {$\#$1}^2 c}{e}+\frac {\text {$\#$1} b}{e}+\frac {a}{e}\& ,3\right ]}}{\text {Root}\left [\text {$\#$1}^3+\frac {\text {$\#$1}^2 c}{e}+\frac {\text {$\#$1} b}{e}+\frac {a}{e}\& ,3\right ]}+c_4\right \}\right \}\] ✓ Maple : cpu = 0.037 (sec), leaf count = 679
dsolve(x*(a*diff(y(x),x)+b*diff(diff(y(x),x),x)+c*diff(diff(diff(y(x),x),x),x)+e*diff(diff(diff(diff(y(x),x),x),x),x))*y(x)=0,y(x))
\[y \left (x \right ) = 0\]