- #1

izen

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## Homework Statement

Solve the integral of differential equation

∫[itex]^{t}_{0}[/itex] y([itex]\tau[/itex]) d[itex]\tau[/itex] -[itex]\acute{y}[/itex] (t) = t

for t≥0 with y(0)=4

## The Attempt at a Solution

take laplace both sides

[itex]\frac{Y}{s}[/itex] - sY + 4 = [itex]\frac{1}{s^{2}}[/itex]

Y [itex]\frac{1 - s^{2}}{s}[/itex] =[itex]\frac{1}{s^{2}}[/itex] - 4

Y [itex]\frac{s^{2}-1}{s}[/itex] =- [itex]\frac{1}{s^{2}}[/itex] + 4

Y = - [itex]\frac{1}{s(s^{2}-1)}[/itex] + [itex]\frac{4s}{s^{2}-1}[/itex]

Partial fraction - [itex]\frac{1}{s(s^{2}-1)}[/itex]

[itex]\frac{1}{s}[/itex] -[itex]\frac{s}{s^{2}-1}[/itex] +[itex]\frac{4s}{s^{2}-1}[/itex]

inverse laplace transform

1-cos(t)+4cos(t) = > 1+3cos(t)

but the answer is 1+[itex]\frac{3}{2}[/itex] (e[itex]^{t}[/itex] + e[itex]^{-t}[/itex])

Please check my solution

Thank you