If `int_a^x ty(t)dt=x^2+y(x),` then find `y(x)`

For x in R, x != 0, if y(x) differential function such that x int_1^x y(t)dt=(x+1)int_1^x t y(t)dt, then y(x) equals:

For x in x != 0, if y(x) differential function such that x int_1^x y(t)dt=(x+1)int_1^x t y(t)dt, then y(x) equals: (where C is a constant.)

For x in R, x != 0, if y(x) differential function such that x int_1^x y(t)dt=(x+1)int_1^x t y(t)dt, then y(x) equals: (where C is a constant.)

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

If y = int_(1)^(x) xsqrt(lnt)dt then find the value of (d^(2)y)/(dx^(2)) at x = e

If int_(0)^(x) f(t)dt=x+int_(x)^(1)t f(t)dt , find the value of f(1).

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^(2)y(x), (x gt 0) is