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(Solved): Solve the Differential equations using Laplace Transform method.   e) Solve \( \mathrm{dx} / ...



Solve the Differential equations using Laplace Transform method.

 

e) Solve \( \mathrm{dx} / \mathrm{dt}+\mathrm{ax}=\mathrm{u}(\mathrm{t}) \) where \( u(t)=\left\{\begin{array}{l}b, 0 \leq t<

e) Solve \( \mathrm{dx} / \mathrm{dt}+\mathrm{ax}=\mathrm{u}(\mathrm{t}) \) where \( u(t)=\left\{\begin{array}{l}b, 0 \leq t


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Solution:- step 1 e) e) It can be used to solve for the unknown functions (dx/dt, ax-u(t), u(t)) at any time t and gives us an equation for each function. In this case, we have two differentials, dx/dt and ax-u(t). We will use them in reverse order:
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