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Verify that the indicated function is an explicit solution of the given differential equation. Assume an appropriate interval I of definition for each solution. dy 2 2-30t + 30y= 12; y ====e dt 5 5 When y = dy = dt 2 5 + 30y = 2-30t Thus, in terms of t, dy dt = --e 5 +30(-30) 5

Verify that the indicated function is an explicit solution of the given differential equation. Assume an appropriate interval I of definition for each solution. dy 2 2-30t + 30y= 12; y ====e dt 5 5 When y = dy = dt 2 5 + 30y = 2-30t Thus, in terms of t, dy dt = --e 5 +30(-30) 5

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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Verify that the indicated function is an explicit solution of the given differential equation. Assume an appropriate interval I of definition for each solution. dy 2 5 dt When y = dy dt = 25 + 30y = + 30y = 12; y = = 2-30t e Thus, in terms of t, dy dt 5 I 2-30t 5 +30 ( ² - e-30²) 5
Transcribed Image Text:Verify that the indicated function is an explicit solution of the given differential equation. Assume an appropriate interval I of definition for each solution. dy 2 5 dt When y = dy dt = 25 + 30y = + 30y = 12; y = = 2-30t e Thus, in terms of t, dy dt 5 I 2-30t 5 +30 ( ² - e-30²) 5
Expert Solution
Step 1: Introduction

Given:

The differential equation is fraction numerator d y over denominator d t end fraction plus 30 y equals 12.

The given function is y equals 2 over 5 minus 2 over 5 e to the power of negative 30 t end exponent.

To Find:

We have to verify that the function y equals 2 over 5 minus 2 over 5 e to the power of negative 30 t end exponent is an explicit solution of the differential equation fraction numerator d y over denominator d t end fraction plus 30 y equals 12.

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