2.1164   ODE No. 1164

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

✓ Mathematica : cpu = 0.011072 (sec), leaf count = 30

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

\[\left \{\left \{y(x)\to c_1 J_v\left (\sqrt {l} x\right )+c_2 Y_v\left (\sqrt {l} x\right )\right \}\right \}\]

✓ Maple : cpu = 0.04 (sec), leaf count = 23

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

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