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The image shows a math exam with various problems. Here's a breakdown of each question for better understanding and solving.

### Problem 1
Find the critical points and classify them (local maximum, local minimum, or saddle point) for the function:

\[
f(x,y) = x^2 + y^2 + 2xy
\]

### Problem 2
Find the solution to the following differential equation:

\[
y' = \frac{1}{x} \left( y + \frac{1}{y} \right)
\]

### Problem 3
Evaluate the double integral:

\[
\iint_{D} (x+y) \, dx\,dy, \quad D = \{(x,y) \, | \, 0 \leq x \leq 1, \, 0 \leq y \leq 1 - x\}
\]

### Problem 4
Solve the differential equation:

\[
y'' + \left( x^2 - 4 \right)y = 0
\]

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The image shows a math exam with various problems.

Explore detailed solutions to university-level math problems, including finding critical points, solving differential equations, and evaluating double integrals. Suitable for advanced mathematics students.

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