2.1200   ODE No. 1200

\[ (1-v) v y(x)+x^2 y''(x)+2 x^2 y'(x)=0 \]

✓ Mathematica : cpu = 0.010915 (sec), leaf count = 62

DSolve[(1 - v)*v*y[x] + 2*x^2*Derivative[1][y][x] + x^2*Derivative[2][y][x] == 0,y[x],x]
 

\[\left \{\left \{y(x)\to c_1 e^{-x} \sqrt {x} J_{\frac {1}{2} (2 v-1)}(-i x)+c_2 e^{-x} \sqrt {x} Y_{\frac {1}{2} (2 v-1)}(-i x)\right \}\right \}\]

✓ Maple : cpu = 0.026 (sec), leaf count = 27

dsolve(x^2*diff(diff(y(x),x),x)+2*x^2*diff(y(x),x)-v*(v-1)*y(x)=0,y(x))
 

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