ODE No. 1162

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

✓ Mathematica : cpu = 0.0298893 (sec), leaf count = 18

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

\[\{\{y(x)\to c_1 J_v(x)+c_2 Y_v(x)\}\}\]

✓ Maple : cpu = 0.013 (sec), leaf count = 15

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

\[y \left (x \right ) = c_{1} \operatorname {BesselJ}\left (v , x\right )+c_{2} \operatorname {BesselY}\left (v , x\right )\]