Find the general solution of this ODE: d²y dy + 14 + 45y 3t? 4 + 2e 2t dt? dt The solution will be of the form: y(t) = Cy1(t) + Dy2(t) + Yp(t) so use C and D as the arbitrary constants. a) The general solution is y(t) =
Find the general solution of this ODE: d²y dy + 14 + 45y 3t? 4 + 2e 2t dt? dt The solution will be of the form: y(t) = Cy1(t) + Dy2(t) + Yp(t) so use C and D as the arbitrary constants. a) The general solution is y(t) =
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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![**Question 4**
**Find the general solution of this ODE:**
\[
\frac{d^2y}{dt^2} + 14\frac{dy}{dt} + 45y = 3t^2 - 4 + 2e^{-2t}
\]
The solution will be of the form:
\[
y(t) = C y_1(t) + D y_2(t) + y_p(t)
\]
so use \( C \) and \( D \) as the arbitrary constants.
**a) The general solution is**
\[
y(t) = \boxed{}
\]
**b) Show your work!**](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffa043fe4-4451-42e8-82d1-21cc59f9ce63%2F8becaedf-a06a-46a2-8265-31ef7a19df5f%2Fi9gxtd_processed.png&w=3840&q=75)
Transcribed Image Text:**Question 4**
**Find the general solution of this ODE:**
\[
\frac{d^2y}{dt^2} + 14\frac{dy}{dt} + 45y = 3t^2 - 4 + 2e^{-2t}
\]
The solution will be of the form:
\[
y(t) = C y_1(t) + D y_2(t) + y_p(t)
\]
so use \( C \) and \( D \) as the arbitrary constants.
**a) The general solution is**
\[
y(t) = \boxed{}
\]
**b) Show your work!**
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