Question

In Problems 11-14 verify that the indicated function is an explicit solution of the given differential equation. Assume an appropriate interval I of definition for each solution 11. 2y' + y = 0; y = e^{-x/2} 12. dy/dt + 20y = 24; y = 6/5 - 6/5 e^{-20t} 13. y'' - 6y' + 13y = 0; y = e^{3x} cos 2x 14. y'' + y = tan x; y = -(cos x)ln(sec x + tan x)

          In Problems 11-14 verify that the indicated function is an explicit solution of the given differential equation. Assume an appropriate interval I of definition for each solution

11. 2y' + y = 0; y = e^{-x/2}

12. dy/dt + 20y = 24; y = 6/5 - 6/5 e^{-20t}

13. y'' - 6y' + 13y = 0; y = e^{3x} cos 2x

14. y'' + y = tan x; y = -(cos x)ln(sec x + tan x)

In Problems 11-14 verify that the indicated function is an explicit solution of the given differential equation. Assume an appropriate interval I of definition for each solution

11. 2y' + y = 0; y = e^-x/2

12. dy/dt + 20y = 24; y = 6/5 - 6/5 e^-20t

13. y” - 6y' + 13y = 0; y = e^3x cos 2x

14. y” + y = tan x; y = -(cos x)ln(sec x + tan x)

Added by Stephen S.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Keondre Parker

07/14/2023

Step 1

**Problem 11:** Given differential equation: \(2y' + y = 0\) Proposed solution: \(y = e^{-x/2}\) **Problem 12:** Given differential equation: \(\frac{dy}{dt} + 20y = 24\) Proposed solution: \(y = \frac{6}{5} - \frac{6}{5} e^{-20t}\) **Problem 13:** Given Show more…

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In Problems 11-14 verify that the indicated function is an explicit solution of the given differential equation. Assume an appropriate interval I of definition for each solution. 11. 2y' + y = 0; y = e^{-x/2} 12. dy/dt + 20y = 24; y = 6/5 - 6/5 e^{-20t} 13. y'' - 6y' + 13y = 0; y = e^{3x} cos 2x 14. y'' + y = tan x; y = -(cos x)ln(sec x + tan x)