ODE3 :=
(64*x^4-96*x^2+8*n*x^4-24*n*x^2+6*n)*y(x)
-2*x*(4*x^4+4*x^2-21)*diff(y(x),x)
+(4*x^4-12*x^2+3)*diff(y(x),x,x);

# Has these solutions:
SolKummerM := (2*x^2-3)*(4+n)*KummerM(-1-1/2*n,1/2,x^2)
-1/4*(4*x^4+4*n*x^4-4*n*x^2-4*x^2-9*n-33)*KummerM(-2-1/2*n,1/2,x^2);
# and
SolKummerU := 2*(n+4)*(n+3)*(2*x^2-3)*KummerU(-1/2*n-1,1/2,x^2)
+(4*x^4*n+4*x^4-4*x^2*n-4*x^2-9*n-33)*KummerU(-1/2*n-2,1/2,x^2);


# Check answer:
odetest(y(x)=SolKummerM, ODE3);
odetest(y(x)=SolKummerU, ODE3);
# Note:
# It takes more CPU time to check the solutions than it did to compute them!

# Can also write the solutions in terms of Cylinder functions:
SolCylU := exp(1/2*x^2)*(
	(4*x^4-36*x^2+4*n*x^4-12*n*x^2+15+3*n)*CylinderU(-n-9/2,2^(1/2)*x)
	+4*2^(1/2)*x*(2*x^2-3)*(4+n)*CylinderU(-n-7/2,2^(1/2)*x));

SolCylV := exp(1/2*x^2)*(
	(4*x^4-36*x^2+4*n*x^4-12*n*x^2+15+3*n)*CylinderV(-n-9/2,2^(1/2)*x)
	+4*x*(2*x^2-3)*CylinderV(-n-7/2,2^(1/2)*x)*2^(1/2));

# Check these solutions too:
odetest(y(x)=SolCylU, ODE3);
odetest(y(x)=SolCylV, ODE3);


# An example with Airy solutions:

EQ := diff(y(x),x,x) + (2-10*x + 4*x^2-4*x^4)*y(x) = 0;
y1 := (2*x^2+x-1)*AiryAi(x^2-1) + (2*x+1)*AiryAi(1,x^2-1);
y2 := (2*x^2+x-1)*AiryBi(x^2-1) + (2*x+1)*AiryBi(1,x^2-1);
odetest(y(x)=y1, EQ);
odetest(y(x)=y2, EQ);