I have confusion on this problem I am working on,
Classify the following integral equation: $$u(x) = \frac{3x}{4} + \frac{1}{5} + \ \int_{0}^{1} (x-t)^3u(t) \,dt$$
I know this Fredholm second kind integral equations because $\phi(x) = 1$ and $f(x) = \frac{3x}{4} + \frac{1}{5}$ and which makes this integral equation nonhomogeneous because $f(x) \neq 0$. And the limits of integration is finite interval and for linearity property $u(x)$ and $u(t)$ have power of one therefore it is linear.
So my answer is Fredholm, Linear, Nonhomogenous. But book's answer has it as Fredholm, Nonlinear, Nonhomogenous. So I am wondering is the book's answer wrong or I am wrong.