The image you uploaded contains handwritten mathematical equations. From what I can see, the expression includes a differential equation and two given functions. Here's what I interpret from the image:

1. The differential equation appears to be: $\frac{d^2 y}{dx^2} - \left(x + x - y\right)^2 - 2 \left(x \frac{dy}{dx} - y\right) = 0$

2. The two functions provided are: $x(t) = e^{t} \sin(t)$ $y(t) = e^{t} \cos(t)$

The task likely involves verifying whether the provided functions $x(t)$ and $y(t)$ satisfy the given differential equation or finding a solution $f(x)$ based on the problem context. Could you clarify if you'd like me to:

1. Solve the differential equation.
2. Verify if the provided functions satisfy the equation.
3. Analyze the system for a specific condition.

Let me know how you'd like to proceed!

Here are 5 related questions and a tip:

1. Would you like me to solve the differential equation step by step?
2. Should I compute derivatives of $x(t)$ and $y(t)$ to verify the equation?
3. Is there a specific initial or boundary condition for this problem?
4. Should I interpret $f(x)$ as a solution function of the differential equation?
5. Are $x(t)$ and $y(t)$ part of a parametric system?

Tip: When working with differential equations, always verify the derivatives and substitutions step by step to avoid small errors!