26. x" +9x=5 cost, x (0) = 0, x'(0) = 0.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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solve the differential equation using the method of undetermined coefficients. If no initial conditions are given, give the general solution.

### Differential Equation Problem

**Problem 26:** Solve the following second-order linear differential equation with constant coefficients:

\[ x'' + 9x = 5\cos t \]

**Initial Conditions:**

- \( x(0) = 0 \)
- \( x'(0) = 0 \)

In this problem, \( x'' \) denotes the second derivative of \( x \) with respect to \( t \). The equation is driven by a cosine function, which acts as the non-homogeneous part. The initial conditions specify that both the function and its first derivative are zero at \( t = 0 \).

### Method of Solution

To solve this differential equation, you may use the method of undetermined coefficients, variation of parameters, or apply the Laplace transform, considering the given initial conditions to find the particular solution that satisfies these constraints.
Transcribed Image Text:### Differential Equation Problem **Problem 26:** Solve the following second-order linear differential equation with constant coefficients: \[ x'' + 9x = 5\cos t \] **Initial Conditions:** - \( x(0) = 0 \) - \( x'(0) = 0 \) In this problem, \( x'' \) denotes the second derivative of \( x \) with respect to \( t \). The equation is driven by a cosine function, which acts as the non-homogeneous part. The initial conditions specify that both the function and its first derivative are zero at \( t = 0 \). ### Method of Solution To solve this differential equation, you may use the method of undetermined coefficients, variation of parameters, or apply the Laplace transform, considering the given initial conditions to find the particular solution that satisfies these constraints.
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