Differential Equations

Edwarm36y0

1. find A,B,C,D in cos(x)/(1+x+x^2)= A+Bx+Cx^2+Dx^3....

2.find (a) Laplace {(t^2)(e^(2t))}, (b) Laplace {f} where f(x) =1 for 0<_x<_1 and f(x)=0 for x>1

PLEASE SHOW ALL WORK.

DO NOT SKIP STEPS.

Please only post answers that you know are CORRECT.

Please use techniques from College Differential Equations or lower courses.

These questions are from one of the following chapters in my Differential Equations text book.

Chapter 7: Laplace Transforms

7.2 Definition of Laplace Transform

7.3 Properties of the Laplace Transform

7.4 Inverse Laplace Transform

7.5 Solving initial value problems

Chapter 8: Series solutions of Differential Equations

8.1 Introduction: The Taylor polynomial approximation

8.2 Power Series and Analytic Function

8.3 Power Series Solutions to Linear Differential Equations.

8.4 Equations with Analytic Coefficients

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