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Solve the initial value problem y=y+t,y(0)=0 using successive approximation method (i.e., de ...
Solve the initial value problem y′=−y+t,y(0)=0 using successive approximation method (i.e., determine ϕn(t) for each integer n>0, and express y=limn→∞ϕn(t) in terms of elementary functions, where ϕn+1(t)=∫0tf(s,ϕn(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: