To use the Laplace transform to solve the given initial value problem, we first take the transform of each dy member of the differential equation + 4y = e. The strategy is that the new equation can be solved for dt Liy} algebraically. Once solved, transforming back to an equation for y gives the solution we need to the original differential equation. dy) + L{4y} = L{e5tz dt We now recall the following, where a and b are constants. • By Theorem 7.2.2.: dy sLiy} - y(0) dt Using linearity of L: L{ay} = aL{y} %3! L{e“} = s- b By Theorem 7.1.1.: Applying these gives the following result. sL{y} - y(0) + S -
To use the Laplace transform to solve the given initial value problem, we first take the transform of each dy member of the differential equation + 4y = e. The strategy is that the new equation can be solved for dt Liy} algebraically. Once solved, transforming back to an equation for y gives the solution we need to the original differential equation. dy) + L{4y} = L{e5tz dt We now recall the following, where a and b are constants. • By Theorem 7.2.2.: dy sLiy} - y(0) dt Using linearity of L: L{ay} = aL{y} %3! L{e“} = s- b By Theorem 7.1.1.: Applying these gives the following result. sL{y} - y(0) + S -
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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