# How to solve ODE with Laplace Transformation and step function?

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Thu Thai on 18 Sep 2020
Answered: Keyur Mistry on 22 Sep 2020
Hello, I have been working on this problem. I have to use Laplace Transformation for this equation:
EQN = D2y+ 5*Dy + y == 8*Du + u (D2y is second order derrivative ). I was told to treat u(t) as a step function, u(t) change from 0 to 1. This is so far my cod % Inverse of the Laplace Transform:
y=ilaplace(Y,s,t)
I compare the result and my code was wrong and I know it must be something with u(t). I need to help to correct the above code. Thank you in advance.

Keyur Mistry on 22 Sep 2020
I understand that the code you have provided is not giving the correct output. After analyzing the code, here are some observations I have
• There is no need to add ‘assume([t Y]>0)’ if we are looking for generalized output
• As u(t) is step function, value of ‘u’ should be equal to ‘heaviside(t)’
• Variable ‘Du’ must be defined the way ‘Dy’ has been defined.