the question is:

Q) Find the general solution of the differential equation dx/dt - x = t+1

A) Here are my workings. Does this look correct?

dx/dt = x + t +1

dx/dt = t(x/t 1 + 1/t)

Let u = x/t 1 + 1/t so du/dx = 1/t so dx = du.t

Equation become: dut/dt = tu

du/u = dt

ln(u) = t + C

u = exp(t + C)

u = Aexp(t)

As u = x/t 1 + 1/t rearranging gives x = ut - t - 1

Putting u into equation gives final answer of x = Aexp(t)t - t - 1