In Exercises 11–52, decide on what substitution to use, and then evaluate the given
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Chapter 6 Solutions
Applied Calculus
- Solve the following equations using Laplace transform; (a) d2x/dt2 + 4 dx/dt + 3x = 2 x(0) = x’(0) = 0 x(t)=? (b) d2x/dt2 + 5 dx/dt + 2x = 1 x(0) = x’(0) = 0 x(t)=?arrow_forwardEvaluate the integral ∫ (3/u +u/4)du =________________________________+ Carrow_forwardFind the kernel of the following differential operator. D3 - 10D2 + 25D = 0arrow_forward
- Use the Laplace transform to solve the following system. ?′′−3?′+?′+2?−?=0?′+?′−2?+?=0 with ?(0)=0,?′(0)=,?(0)=−1.arrow_forwardIn Exercises 1-8 compute an area function A(x) off (x) with lower limita. Then, to verify the FTC II inverse relationship, compute A' (x) and showthat it equals f (x ). f (x) = e-x , a =-1arrow_forwardLet V ∼ exp(7). Write an integral for E[√5 + cos 6V − 2V 2].arrow_forward
- If e is the unity in an integral domain D , prove that (−e)a = −a for a D .arrow_forwardIn Exercises 3–6, write a in the form a = aTT + aNN at the given value of t without finding T and N.arrow_forwardUse the Laplace transforms to solve the following initial value problem. x"+6x'+25x = 0; x(0)=2, x'(0)=5arrow_forward
- Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning