int_(0)^(x)t*y(t)dt=x^(3)y(x),(x>0)

A curve passing through (2,3) and satisfying the differential equation int_(0)^(x)ty(t)dt=x^(2)y(x),(x>0) is

A curve passing through (2,3) and satisfying the differential equation int_0^x ty(t)dt=x^2y(x),(x >0) is

If int_(0)^(x)f(t)dt=x^(2)+int_(x)^(1)t^(2)f(t)dt, then f'((1)/(2)) is

If int_(0)^(x) f(t)dt=x^(2)+2x-int_(0)^(x) tf(t)dt, x in (0,oo) . Then, f(x) is

If int_(0)^(x) f(t)dt=x^(2)+2x-int_(0)^(x) tf(t)dt, x in (0,oo) . Then, f(x) is

For x in x!=0, if y(x) differential function such that x int_(1)^(x)y(t)dt=(x+1)int_(1)^(x)ty(t)dt then y(x) equals: (where C is a constant.)

A differentiable function y=g(x) satisfies int_(0)^(x)(x-t+1)g(t)dt=x^(4)+x^(2) for all x>=0 then y=g(x) satisfies the differential equation

If int_(0)^(x)f(t)dt = x^(2)-int_(0)^(x^(2))(f(t))/(t)dt then find f(1) .

If int_(0)^(x)f(t)dt=e^(x)-ae^(2x)int_(0)^(1)f(t)e^(-t)dt , then

If int_(0)^(x)f(t)dt=e^(x)-ae^(2x)int_(0)^(1)f(t)e^(-t)dt , then