2.1153   ODE No. 1153

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

✓ Mathematica : cpu = 0.0160514 (sec), leaf count = 56

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

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

✓ Maple : cpu = 0.052 (sec), leaf count = 31

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

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