Question

Using appropriate auxiliary variables, write the third order ODE d^3u/dt^3 + 2d^2u/dt^2 - 3du/dt + u = 4e^t as a system of three first order differential equations, and express your system in matrix form.

          Using appropriate auxiliary variables, write the third order ODE

d^3u/dt^3 + 2d^2u/dt^2 - 3du/dt + u = 4e^t

as a system of three first order differential equations, and express your system in matrix form.

Added by Lisa S.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Madhur L

08/16/2023

Step 1

Now, we can rewrite the given third-order ODE in terms of these auxiliary variables: $\frac{d^3u}{dt^3} + 2\frac{d^2u}{dt^2} + 3\frac{du}{dt} + u = 4e^t$ Substitute the auxiliary variables: $\frac{dv_3}{dt} + 2v_3 + 3v_2 + v_1 = 4e^t$ Now, we can write the Show more…

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Using appropriate auxiliary variables, write the third order ODE d^3u/dt^3 + 2(d^2u/dt^2) + du/dt + u = 4e^t as a system of three first order differential equations, and express your system in matrix form.