Q3// The question in the image Given the following differential equation:Y – 7æ² sin²(ny") = 7x² cos (Ty/")What is y (2) if y(0) = 9?(Please give your answer with four decimals.)Answer:

Name: Q3// The question in the image Given the following differential equati
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Description: Q3// The question in the image Given the following differential equation:Y – 7æ² sin²(ny") = 7x² cos (Ty/")What is y (2) if y(0) = 9?(Please give your answer with four decimals.)Answer:

Answered: Given the following differential…

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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Q3// The question in the image

Given the following differential equation:
Y – 7æ² sin²(ny") = 7x² cos (Ty/")
What is y (2) if y(0) = 9?
(Please give your answer with four decimals.)
Answer:

Expert Solution

Step 1

We need to find the solution of the following given differential equation.

Step 2

The important key: sin²t + cos²t = 1.

Here,

y' - 7x² sin²(πy'') = 7x² cos²(πy'')

=> y' = 7x² sin²(πy'') + 7x² cos²(πy'')

=> y' = 7x² (sin²(πy'') + cos²(πy''))

=> y' = 7x² (1)

=> y' = 7x²

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