ODE No. 1272

$$(4a^2{x}^2+1)y(x)+4x^2{y}^{″}(x)=0$$ ✓ Mathematica : cpu = 0.0089455 (sec), leaf count = 32

DSolve[(1 + 4*a^2*x^2)*y[x] + 4*x^2*Derivative[2][y][x] == 0,y[x],x]
 

$$\left\{\{y(x)\to c_1\sqrt{x}{J}_0(ax)+c_2\sqrt{x}{Y}_0(ax)\}\right\}$$ ✓ Maple : cpu = 0.034 (sec), leaf count = 23

dsolve(4*x^2*diff(diff(y(x),x),x)+(4*a^2*x^2+1)*y(x)=0,y(x))
 

$$y\left(x\right)=\sqrt{x}(\mathrm{BesselY}(0,ax)c_2+\mathrm{BesselJ}(0,ax)c_1)$$