Please work out the step-by-step process of how you get to the solution on paper, please. The answer is given, I just want to see the work done that teaches how to get the solution. *See Image. Substituting these expressions into the system shown earlier yields the following system.\[(\cos 5t)v_1' + (\sin 5t)v_2' = 0\]\[(-5 \sin 5t)v_1' + (5 \cos 5t)v_2' = 4 \sec 5t\]Solve this system for \( v_1'(t) \) and \( v_2'(t) \).\[v_1'(t) = -\frac{4}{5} \tan 5t\]\[v_2'(t) = \frac{4}{5}\]

The given system of differential equations has two functions v1 and v2. Both are the functions of…

Answered: Substituting these expressions into the…

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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Please work out the step-by-step process of how you get to the solution on paper, please. The answer is given, I just want to see the work done that teaches how to get the solution. *See Image.

Substituting these expressions into the system shown earlier yields the following system.

\[
(\cos 5t)v_1' + (\sin 5t)v_2' = 0
\]

\[
(-5 \sin 5t)v_1' + (5 \cos 5t)v_2' = 4 \sec 5t
\]

Solve this system for \( v_1'(t) \) and \( v_2'(t) \).

\[
v_1'(t) = -\frac{4}{5} \tan 5t
\]

\[
v_2'(t) = \frac{4}{5}
\]

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