'diff(y,x,2) + y;

'diff(y,x,2) + 'diff(y,x);

x^2 * 'diff(y,x,2) + (1 - a - b) * x * 'diff(y,x) + a*b * y;

9 * x^2 * 'diff(y,x,2) + 9*x^2 * 'diff(y,x) + 2 * y;

2*x*(x - 1) * 'diff(y,x,2) + 3*(x - 1) * 'diff(y,x) - y;

x^2 * 'diff(y,x,2) + x * 'diff(y,x) + x^2 * y;

x* 'diff(y,x,2) + 'diff(y,x) - 4 * y;

x^2 * 'diff(y,x,2) + (x^2 + x) * 'diff(y,x) - y;

3*x*'diff(y,x,2) + (2-x) * 'diff(y,x) - y;

4 * x^2 * 'diff(y,x,2) + 2*x^2 * 'diff(y,x) - (x + 3) * y;

x^2 * 'diff(y,x,2) + (x^2 - x) * 'diff(y,x) + y;

x * 'diff(y,x,2) - 'diff(y,x) - x* y;

3 * x^2 * 'diff(y,x,2) + 8 * x * 'diff(y,x) + (x-2) * y;

x * 'diff(y,x,2) + (x-1)*'diff(y,x) - 2 * y;

x*(x+1) * 'diff(y,x,2) + (x+5) * 'diff(y,x) - 4 * y;

x * 'diff(y,x,2) + (1-x)* 'diff(y,x) - y;

x^2 * 'diff(y,x,2) -  x* (1 + x) * 'diff(y,x) + y;

3*x*'diff(y,x,2) + 2*(1-x) * 'diff(y,x) - 4 * y;

x * 'diff(y,x,2) + (x+2) * 'diff(y,x) - y;

x*(1-x) * 'diff(y,x,2) + (1/2 - 4*x) * 'diff(y,x) - 2 * y;

3*x*(1-x)*'diff(y,x,2) + (1-27*x)*'diff(y,x) - 45*y;

2*x*(1-x) * 'diff(y,x,2) + (1-6*x) * 'diff(y,x) - 2*y;

2*x*(1-x) * 'diff(y,x,2) + (3-10*x) * 'diff(y,x) - 6 *y;

x*(1-x)*'diff(y,x,2) + (1 - 3*x) * 'diff(y,x) - y;

x*(1-x)* 'diff(y,x,2) + (2-2*x)*'diff(y,x) - y/4;

4*x^2*'diff(y,x,2) + 4*x* 'diff(y,x) + (4*x^2-1)*y;

9*x^2* 'diff(y,x,2) + 9*x*'diff(y,x) + (9*x^2 - 16) * y;

x^2 * 'diff(y,x,2) + x* 'diff(y,x) + (x^2-1)*y;

x^2*'diff(y,x,2) + x*'diff(y,x) + x^2 * y;

9*x^2*'diff(y,x,2) + 9*x * 'diff(y,x) + (9*x^2 - 4)*y;

x^2 * 'diff(y,x,2) + x*'diff(y,x) + (x^2-16) * y;

x^2 * 'diff(y,x,2) + x*'diff(y,x) + (x^2-1) * y;

x^2 * 'diff(y,x,2) + x*'diff(y,x) + (x^2-4)*y;

'diff(y,x,2) + 5 * 'diff(y,x) + 6*y;

'diff(y,x,2) + 8 * 'diff(y,x) + 16 * y;

'diff(y,x,2) + 'diff(y,x) - y;

2 * 'diff(y,x,2) + 7 * 'diff(y,x) - 4* y;

'diff(y,x,2) - 'diff(y,x) - 11 * y;

4 * 'diff(y,x,2) + 20 * 'diff(y,x) + 25 * y;

'diff(y,x,2) - 8 * 'diff(y,x) + 7 * y;

'diff(y,x,2) + 4*'diff(y,x) + 8*y;

'diff(y,x,2) + 10 * 'diff(y,x) + 25 * y;

'diff(y,x,2) + 7 * y;

'diff(y,x,2) + 2 * 'diff(y,x) + 5 * y;

'diff(y,x,2) -2*'diff(y,x) + 26 * y;

x^2 * 'diff(y,x,2) + 6 * x * 'diff(y,x) + 6 * y;

2 * x^2 * 'diff(y,x,2) + 13 * x * 'diff(y,x) + 15 * y;

x^2 * 'diff(y,x,2) - x * 'diff(y,x) + 17 * y;

x^2 * 'diff(y,x,2) + 2 * 'diff(y,x) - 3 * y;

4 * x^2 * 'diff(y,x,2) + 2 * x^2 * 'diff(y,x) - (x+3) * y;

x^2 * 'diff(y,x,2) + (x^2-x)*'diff(y,x) + y;

x*'diff(y,x,2) - 'diff(y,x) - x*y;

3 * x^2 * 'diff(y,x,2) + 8 * x * 'diff(y,x) + (x-2) * y;

x* 'diff(y,x,2) + (x-1) * 'diff(y,x) - 2 * y;

x * (x + 1) * 'diff(y,x,2) + (x + 5) * 'diff(y,x) - 4 * y;

x * 'diff(y,x,2) + (1- x) * 'diff(y,x) - y;

x^2 * 'diff(y,x,2) - x * (1 + x) * 'diff(y,x) + y;

3 * x * 'diff(y,x,2) + 2*(1-x)*'diff(y,x) - y;

'diff(y,x,2) + (b^2 - (4 * n^2 - 1))/(4 * x^2) * y;

'diff(y,x,2) + (1-2*a) * 'diff(y,x) / x + (b^2 + (a^2 - n^2)/x^2) * y;

'diff(y,x,2) + b^2 * x^3 * y;

'diff(y,x,2) + b^2 * x^2 * y;

'diff(y,x,2) + 'diff(y,x) / x + 4 * (x^2 - n^2 / x^2) * y;

'diff(y,x,2) + 'diff(y,x) / x + (1 - n^2/x) * y / (4 * x);

'diff(y,x,2) + (1- n) * 'diff(y,x)/ x + y / (4 * x);

'diff(y,x,1) = -((x^9+4*x^7+6*x^5+4*x^3+x)*'diff(y,x,2) 
             +(-100*x^7-200*x^5-96*x^3)*y) /(x^8+2*x^6-2*x^2-1);

'diff(y,x,2) = -((x^10+x^8-10*x^6+14*x^4-7*x^2+1)*'diff(y,x,1) 
	     +(x^7+3*x^5+3*x^3+x)*y)/(x^11-3*x^9+2*x^7+2*x^5-3*x^3+x);

'diff(y,x,2) = -((x^10+3*x^9+2*x^8-7*x^7-25*x^6-40*x^5-43*x^4-31*x^3-16*x^2-5*x-1)
		    *'diff(y,x,1) +(x^7-3*x^5+3*x^3-x)*y)
		    /(x^11+4*x^10+9*x^9+12*x^8+9*x^7-9*x^5-12*x^4-9*x^3-4*x^2-x);

'diff(y,x,2) = (2*x*'diff(y,x,1)-2*y)/x^2;

'diff(y,x,2) = -((x^3-5*x^2+4*x)*'diff(y,x,1)+(-x^2+5*x-4)*y)/(x^3-2*x^2);

'diff(y,x,2) = ((x^5-4*x^4+8*x^3-4*x^2-x)*'diff(y,x,1)
		   +(-x^4+4*x^3-8*x^2+4*x+1)*y)
		   /(x^5-3*x^4+2*x^3-4*x^2+x-1);

'diff(y,x,2) = ((4*x^5-8*x^4+(15-4*b)*x^3+(4*b-15)*x^2+(4-b)*x)
		    *'diff(y,x,1)
		    +((8*a-8)*x^4+(16-12*a)*x^3+(8*b+6*a-26)*x^2+(-8*b-a+24)*x
				 +2*b-6) *y)
		    /(2*x^4-3*x^3+x^2);

'diff(y,x,2) = ((4*a*x^4-8*a*x^3+(7*a-4)*x^2+(4-3*a)*x-1)*'diff(y,x,1)
		    +(8*a^2*x^3-12*a^2*x^2+6*a^2*x-a^2)*y)
		    /(2*a*x^3-3*a*x^2+a*x);

'diff(y,x,2) = (((8*a-6)*x^6+(24*a-18)*x^5+(42*a-34)*x^4+(44*a-38)*x^3
				   +(30*a-27)*x^2+(12*a-11)*x+2*a-1)
		    *'diff(y,x,1) +(8*a*x^3+12*a*x^2+6*a*x+a)*y)
		    /(2*x^7+7*x^6+15*x^5+20*x^4+19*x^3+12*x^2+5*x+1);

'diff(y,x,2) = -(((u+n+1)*x-k)*'diff(y,x,1)+n*u*y)/(x^2-x);

'diff(y,x,2) = -(((u+n+1)*x-15*u-15*n+3*k-15)*'diff(y,x,1)+n*u*y)
		   /(x^2-27*x+180);

'diff(y,x,2) = -((2*x^3-k*x^2+(u+n-1)*x)*'diff(y,x,1)
		   +(x^3+(1-k)*x^2+(u+n-1)*x-n*u)*y) /(x^3-x^2);

'diff(y,x,2) = -((18*x^3-69*x^2+96*x)*'diff(y,x,1)
		   +(9*x^3-60*x^2+115*x-304)*y)/(9*x^3-9*x^2);

'diff(y,x,2) = -((46*x^4-92*x^3+32*x^2+14*x-7)*'diff(y,x,1)
		    +(240*x^3-360*x^2+180*x-30)*y)/(2*x^5-5*x^4+2*x^3+2*x^2-x);

'diff(y,x,2) = ((5*x^2-20*x+15)*'diff(y,x,1)+30*y)/(x^3-4*x^2+5*x-2);

'diff(y,x,2) = -(((b+2*a+1)*x-b-2*a-8)*'diff(y,x,1)+(a*b+a^2)*y)/(x^2-3*x+2);

'diff(y,x,2) = -(((8*a+2)*x^4+(16*a+4)*x^3+(14*a+5)*x^2+(6*a+3)*x+a+1)
		    *'diff(y,x,1)+(8*a^2*x^3+12*a^2*x^2+6*a^2*x+a^2)*y)
		    /(2*x^5+5*x^4+6*x^3+4*x^2+x);

'diff(y,x,2) = -(8*x*'diff(y,x,1)+(2*x^2-1)*y)/(2*x^2-2);

'diff(y,x,2) = -((2*x^5+6*x^3)*'diff(y,x,1)+(6*x^2-28)*y)/(x^6-x^4);

'diff(y,x,2) = -((2*x^5-10*x^4+26*x^3-38*x^2+28*x-8)*'diff(y,x,1)
		    +(6*x^2-12*x-22)*y)/(x^6-6*x^5+14*x^4-16*x^3+9*x^2-2*x);

'diff(y,x,2) = -((8*x^4-16*x^3+12*x^2-4*x)*'diff(y,x,1)
		   +(8*x^5-20*x^4-6254*x^3+9401*x^2-4703*x+784)*y)
		   /(8*x^5-20*x^4+16*x^3-4*x^2);

'diff(y,x,2) = (-x^2*'diff(y,x,1)-(2-933156*x)*y)/x^3;

'diff(y,x,2) = (x^6-x^5+x^4-4*x^3-x^2+x-1)*'diff(y,x,1)/(x^6-x^2);

'diff(y,x,2) = ((x^7-2*x^6+x^5-6*x^4-x^3-x)*'diff(y,x,1)
		   +(x^6+3*x^4+3*x^2+1)*y)/(x^7-x^3);

'diff(y,x,2) = ((2*x^7-x^6+2*x^5-6*x^4-2*x^3+3*x^2-2*x)*'diff(y,x,1)
		   +(2*x^6+6*x^4+6*x^2+2)*y)/(2*x^7-2*x^3);

'diff(y,x,2) = -(4*x^4*'diff(y,x,1)-8*a*x^3*'diff(y,x,1)
	      	+4*a^2*x^2*'diff(y,x,1)+a^2*'diff(y,x,1)-4*x^3*y+6*a*x^2*y
		  -2*a^2*x*y+a^2*y)/(2*x*(x-a)*(2*x^2-2*a*x+2*x-a));

'diff(y,x,2) = (((2*a+1)*x^3-4*a*x^2+(2*a-1)*x)*'diff(y,x,1)
		   +(((-a-1)*a-a-1)*x^2+(a*(2*a+1)+a-1)*x-a^2)*y)
		   /(x^4-2*x^3+x^2);

(x^2-1)*'diff(y,x,2)-2*x*'diff(y,x,1)+2*y;

4*x^2*'diff(y,x,2)+4*x*'diff(y,x,1)-y;

'diff(y,x,2) + 2 * 'diff(y,x) - 15* y;

x * 'diff(y,x,2) - (x+1)*'diff(y,x) + y;

x * 'diff(y,x,2) + (1-2*x) *'diff(y,x) + (x-1)*y;

'diff(y,x,2) -2*x * 'diff(y,x) + n*y;

(1-x^2) * 'diff(y,x,2) - 2 * x * 'diff(y,x) + n * (n + 1) * y;

x * 'diff(y,x,2) + (1-x) * 'diff(y,x) + n * y;