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KHITISH BISWAL Grade: 12
        

using laplace transformation


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


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

7 years ago

Answers : (1)

Badiuddin askIITians.ismu Expert
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!/s   + 2/s2


[s2 L(y) -4s -2 ] + [sL(y)-4] =2!/s   + 2/s2


 [s2 +s]L(y) =2!/s   + 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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Badiuddin



7 years ago
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