2.1551   ODE No. 1551

2(ν2x2+6)y(x)+ν2(ν2x2+4)y(x)+x2y(4)(x)=0

Mathematica : cpu = 0.324606 (sec), leaf count = 110

DSolve[nu^2*(4 + nu^2*x^2)*y[x] - 2*(6 + nu^2*x^2)*Derivative[2][y][x] + x^2*Derivative[4][y][x] == 0,y[x],x]
 
{{y(x)c3(1x)eνx(ν2x2+ν2x+ν2+6νx+6ν+15)x+c4(1x)eνx(ν2x2+ν2x+ν26νx6ν+15)x+c1eνxx+c2eνxx}}

Maple : cpu = 0.247 (sec), leaf count = 62

dsolve(x^2*diff(diff(diff(diff(y(x),x),x),x),x)-2*(nu^2*x^2+6)*diff(diff(y(x),x),x)+nu^2*(nu^2*x^2+4)*y(x)=0,y(x))
 
y(x)=(c4ν2x3+6c4νx2+15c4x+c2)eνx+eνx(c3ν2x36c3νx2+15c3x+c1)x