What is the solution to the equation y'' - 3y' + 2y = 0?

₹0.0

Question: What is the solution to the equation y\'\' - 3y\' + 2y = 0?

Options:

Correct Answer: y = C1 e^(x) + C2 e^(2x)

Solution:

The characteristic equation r^2 - 3r + 2 = 0 has roots 1 and 2, leading to y = C1 e^(x) + C2 e^(2x).

What is the solution to the equation y'' - 3y' + 2y = 0?

What is the solution to the equation y'' - 3y' + 2y = 0?

Step 1: Identify the given differential equation, which is y'' - 3y' + 2y = 0.
Step 2: Write the characteristic equation by replacing y'' with r^2, y' with r, and y with 1. This gives us r^2 - 3r + 2 = 0.
Step 3: Factor the characteristic equation r^2 - 3r + 2. It factors to (r - 1)(r - 2) = 0.
Step 4: Solve for r by setting each factor equal to zero. This gives us r - 1 = 0 (so r = 1) and r - 2 = 0 (so r = 2).
Step 5: Write the general solution using the roots found. The general solution is y = C1 e^(1x) + C2 e^(2x), where C1 and C2 are constants.

No concepts available.