ODE No. 1305

\[ x^3 y''(x)+2 x y'(x)-y(x)=0 \] Mathematica : cpu = 0.0748979 (sec), leaf count = 47

DSolve[-y[x] + 2*x*Derivative[1][y][x] + x^3*Derivative[2][y][x] == 0,y[x],x]
 

\[\left \{\left \{y(x)\to c_2 G_{1,2}^{2,0}\left (-\frac {2}{x}|\begin {array}{c} \frac {1}{2} \\ -1,0 \\\end {array}\right )+c_1 e^{\frac {1}{x}} \left (I_0\left (\frac {1}{x}\right )-I_1\left (\frac {1}{x}\right )\right )\right \}\right \}\] Maple : cpu = 0.056 (sec), leaf count = 44

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

\[y \left (x \right ) = \left (-c_{2} \BesselK \left (1, -\frac {1}{x}\right )+c_{2} \BesselK \left (0, -\frac {1}{x}\right )+c_{1} \left (\BesselI \left (0, \frac {1}{x}\right )-\BesselI \left (1, \frac {1}{x}\right )\right )\right ) {\mathrm e}^{\frac {1}{x}}\]