2.1564   ODE No. 1564

(12n24x4+3)y(x)(4n2+3)x2y(x)+(12n23)xy(x)+x4y(4)(x)+4x3y(3)(x)=0

Mathematica : cpu = 1.03295 (sec), leaf count = 230

DSolve[(3 - 12*n^2 - 4*x^4)*y[x] + (-3 + 12*n^2)*x*Derivative[1][y][x] - (3 + 4*n^2)*x^2*Derivative[2][y][x] + 4*x^3*Derivative[3][y][x] + x^4*Derivative[4][y][x] == 0,y[x],x]
 
{{y(x)14c1x0F3(;12,32n2,n2+32;x464)22+c3(1)14(2n1)22n+12(2n+1)+1x2n10F3(;1n,12n2,n2;x464)+c4(1)14(2n1)212(12n)2n+1x2n10F3(;n2+12,n2,n+1;x464)+(1)3/4c2x30F3(;32,2n2,n2+2;x464)162}}

Maple : cpu = 0.279 (sec), leaf count = 88

dsolve(x^4*diff(diff(diff(diff(y(x),x),x),x),x)+4*x^3*diff(diff(diff(y(x),x),x),x)-(4*n^2+3)*x^2*diff(diff(y(x),x),x)+(12*n^2-3)*x*diff(y(x),x)-(4*x^4+12*n^2-3)*y(x)=0,y(x))
 
y(x)=c4x2hypergeom([],[12,n2+32,32n2],x464)+c3x4hypergeom([],[32,n2+2,n2+2],x464)+c2KelvinBei(n,x)2+KelvinBer(n,x)2c2+c1(KelvinBer(n,x)2+KelvinBei(n,x)2)x