can someone work on this lab exercise. please see attached. thank you 

 ATTACHMENT PREVIEW Download attachmentMath 270Name______________________________Lab #7This week, we study Laplace Transforms, one of the most useful transforms in all of mathematics,because they allow us to move from the “differential equation” space or domain to an algebraicdomain, operate algebraically to a solution, and then transform back into differential equation space toprovide the answer.Throughout the Lab, show all your intermediate steps.First, some review questions.1.)An inductor in an electric circuit has voltage operating asVL=20−.2tfor a 4 H inductor.Find the current in the circuit after 10 seconds if the initial current is575 mA.(Note: useVL=Ldi/dtas the base for your calculations.)2.)Find the first 5 terms of the sequence:a¿n=125(15)n−1+(3n−7), n = 1,2,3,4, and 5. (Payattention to the values of n in this case)

View the AnswerMath 270Name______________________________Lab #73.)Find the Taylor Series approximation forf(x)=cos(−x)wheren=5anda=¿4.4.)Solve the differential equationy’−2y=2x+exFirst question: which method are you goingto use to solve it?

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