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Solve the initial value problem $y_{′}=−y+t,y(0)=0$ using successive approximation method (i.e., determine $ϕ_{n}(t)$ for each integer $n>0$, and express $y=lim_{n→∞}ϕ_{n}(t)$ in terms of elementary functions, where $ϕ_{n+1}(t)=∫_{0}f(s,ϕ_{n}(s))ds)$.

To solve the given initial value problem using the successive approximation method, we'll follow the steps:

Step 1: Express the differential equation in the form . Given: