Question

solve it y" - ty' + y = 1 if y(0) = 1 , y '(0) = 2​

Answer 1

Answer:

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Answer 2

Answer:

ty′′−ty′+y=1

−(s2L(y)−sy(0)−y′(0))′+(sL(y)−y(0))′+L(y)=1s

(s−s2)L′(y)+(2−2s)L(y)=1s

L′(y)+2sL(y)=1s2(1−s)

with integrating factor s2 we have

(s2L(y))′y=11−s=L−1−ln(1−s)s2+Ct=∫t0exx(t−x)dx+Ct=t∫t0exxdx−et+1+Ct=tEi(t)−et+1+