5. Laplace Transforms (a) Use the theorem of derivatives of Laplace transforms to: i. 2ks (s²-k²)2. (b) Use the Laplace Transform to solve the following ODES: i. x" + 4x cost, x(0) = 0 = x'(0); x" - 4x = 3t, x(0) = 0 = x¹(0). ii. compute L[cosh kt] directly from the formula for L[sinh kt]; show that C[t sinhkt ii. = =
5. Laplace Transforms (a) Use the theorem of derivatives of Laplace transforms to: i. 2ks (s²-k²)2. (b) Use the Laplace Transform to solve the following ODES: i. x" + 4x cost, x(0) = 0 = x'(0); x" - 4x = 3t, x(0) = 0 = x¹(0). ii. compute L[cosh kt] directly from the formula for L[sinh kt]; show that C[t sinhkt ii. = =
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter9: Multivariable Calculus
Section9.2: Partial Derivatives
Problem 33E
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