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clc
disp(' y^(1/m)+y^-(1/m)=2x ');
disp(' OR y^(2/m)-2xy^(1/m)+1');
disp('OR y=[x+(x^2-1)]^m and y=[x-(x^2-1)]^m ');
syms x m
disp('For y=[x+(x^2-1)]^m ');
y=(x+(x^2-1))^m
disp('we have to prove (x^2-1)y(n+2)+(2n+1)xy(n+1)+(n^2-m^2)yn ') ;
//n=input('Enter the order of differentiation ");
disp('calculating yn for various values of n');
for n=1:4
//yn=diff(F,x,n)
F=(x^2-1)*diff(y,x,n+2)+(2*n+1)*x*diff(y,x,n+1)+(n^2-m^2)*diff(y,x,n);
disp(n);
disp('the expression for yn is ');
disp(F);
disp('Which is equal to 0 ');
end
disp('For y=[x-(x^2-1)]^m ');
y=(x-(x^2-1))^m
disp('we have to prove (x^2-1)y(n+2)+(2n+1)xy(n+1)+(n^2-m^2)yn ') ;
//n=input('Enter the order of differentiation ");
disp('calculating yn for various values of n');
for n=1:4
//yn=diff(F,x,n)
F=(x^2-1)*diff(y,x,n+2)+(2*n+1)*x*diff(y,x,n+1)+(n^2-m^2)*diff(y,x,n);
disp(n);
disp('the expression for yn is ');
disp(F);
disp('Which is equal to 0 ');
end
disp('Hence proved');
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