I will analyze the text in the uploaded image to extract the mathematical content and provide solutions or explanations. Please hold on for a moment while I process it.The image contains a mathematical problem. Let me extract the content and provide the solution.

Extracted Problem

The image appears to show a function-related problem. Here's the relevant part extracted from the text:

Part (a): $y'' - 2y' + 2y = 0$ Find the general solution.

Solution for Part (a):

The differential equation is a second-order linear homogeneous differential equation with constant coefficients:

$y'' - 2y' + 2y = 0$

To solve it, we start by finding the characteristic equation:

$r^2 - 2r + 2 = 0$

We solve this quadratic equation using the quadratic formula:

$r = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

Here, $a = 1$, $b = -2$, and $c = 2$. Substituting these values in:

[ r = \frac{-(-2) \pm \sqrt{(-2)^2 -