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

using laplace transformation


solve d^2y/dt + dy/dt = t^2 + 2t


Given that y(0) = 4, y'(o)=2

Grade:12

1 Answers

Badiuddin askIITians.ismu Expert
148 Points
14 years ago

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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Askiitians Experts
Badiuddin

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