For x ∈ R, x ≠ 0, if y(x) is a differentiable function such that x ∫_1^x y(t) d t=(x+1) ∫_1^x t y(t) d t, then y(x) equals: (where C is a constant.)

For $\displaystyle x \in \mathbf{R}, x \neq 0$, if $\displaystyle y(x)$ is a differentiable function such that $\displaystyle x \int_1^x y(t) d t=(x+1) \int_1^x t y(t) d t$, then $\displaystyle y(x)$ equals : (where C is a constant.)