2.1306   ODE No. 1306

\[ y(x) \left (a x^2+a+b x\right )+x^3 y''(x)+x^2 y'(x)=0 \]

✗ Mathematica : cpu = 0.557351 (sec), leaf count = 0

DSolve[(a + b*x + a*x^2)*y[x] + x^2*Derivative[1][y][x] + x^3*Derivative[2][y][x] == 0,y[x],x]
 

, DifferentialRoot result

\[\left \{\left \{y(x)\to (x)\right \}\right \}\]

✓ Maple : cpu = 0.234 (sec), leaf count = 69

dsolve(x^3*diff(diff(y(x),x),x)+x^2*diff(y(x),x)+(a*x^2+b*x+a)*y(x)=0,y(x))
 

\[y \left (x \right ) = \operatorname {HeunD}\left (0, 8 a +4 b , 0, 8 a -4 b , \frac {1+x}{x -1}\right ) \left (\left (\int \frac {1}{x \operatorname {HeunD}\left (0, 8 a +4 b , 0, 8 a -4 b , \frac {1+x}{x -1}\right )^{2}}d x \right ) c_{2} +c_{1} \right )\]