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```        using laplace transformation
solve d^2y/dt + dy/dt = t^2 + 2t
Given that y(0) = 4, y'(o)=2```
7 years ago

147 Points
```										Dear KHITISH
d2y/dt2 + dy/dt = t^2 + 2t
take laplace
[s2 L(y) -sy(0) -y'(0) ] + [sL(y)-y(o)] =2!/s3    + 2/s2
[s2 L(y) -4s -2 ] + [sL(y)-4] =2!/s3    + 2/s2
[s2 +s]L(y) =2!/s3    + 2/s2  +4s +6
L(y) =2/s4(s+1)   + 2/s3(s+1)   + 4/(s+1)      +6/s(s+1)
=2/s4  +6/s -2/(s+1)
now take inverse
y = 2t3/3!  + 6   -2e-t
=t3/3 + 6   -2e-t
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```
7 years ago
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