2.1217   ODE No. 1217

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

✓ Mathematica : cpu = 0.0503701 (sec), leaf count = 30

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

\[\left \{\left \{y(x)\to c_1 \sec (x) J_{\sqrt {a}}(x)+c_2 \sec (x) Y_{\sqrt {a}}(x)\right \}\right \}\]

✓ Maple : cpu = 0.077 (sec), leaf count = 22

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

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