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Using the Laplace transform method, solve for t> 0 the following differential equation: d²x dx + 5a + 6Bx = 0, dt2 dt subject to x(0) = xo and i(0) = ¢o. In the given ODE, a and ß are scalar coefficients. Also, xo and io are values of the initial conditions. Moreover, it is known that x(t) a + Bx = 0. = 2e-/2(cos(t) – 24 sin(t)) is a solution of ODE + dt2

Using the Laplace transform method, solve for t> 0 the following differential equation: d²x dx + 5a + 6Bx = 0, dt2 dt subject to x(0) = xo and i(0) = ¢o. In the given ODE, a and ß are scalar coefficients. Also, xo and io are values of the initial conditions. Moreover, it is known that x(t) a + Bx = 0. = 2e-/2(cos(t) – 24 sin(t)) is a solution of ODE + dt2

Advanced Engineering Mathematics
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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Question
Using the Laplace transform method, solve for t> 0 the following differential equation: d²x dx + 5a- + 6,3x 0, dt? dt subject to x(0) = xo and ¿(0) = ¢o. In the given ODE, a and ß are scalar coefficients. Also, xo and io are values of the initial conditions. Moreover, it is known that x(t) = 2e-t/2(cos(t) – 2 sin(t)) is a solution of ODE + Bx = 0. + dt2 dx dt Your answer must contain detailed explanation, calculation as well as logical argumentation leading to the result. If you use mathematical theorem(s)/property(-ies) that you have learned par- ticularly in this unit, clearly state them in your answer.
Transcribed Image Text:Using the Laplace transform method, solve for t> 0 the following differential equation: d²x dx + 5a- + 6,3x 0, dt? dt subject to x(0) = xo and ¿(0) = ¢o. In the given ODE, a and ß are scalar coefficients. Also, xo and io are values of the initial conditions. Moreover, it is known that x(t) = 2e-t/2(cos(t) – 2 sin(t)) is a solution of ODE + Bx = 0. + dt2 dx dt Your answer must contain detailed explanation, calculation as well as logical argumentation leading to the result. If you use mathematical theorem(s)/property(-ies) that you have learned par- ticularly in this unit, clearly state them in your answer.
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