The image contains three differential equations labeled 1, 2, and 3. I'll analyze each one and solve them. Here's a breakdown:

1. Differential Equation:

$\frac{dy}{dx} = \frac{2x - y}{x + 4y}, \quad y(1) = 1$ This is a first-order nonlinear differential equation. It can potentially be solved using substitution methods or as a homogeneous equation. Let's proceed to solve it step by step.

2. Differential Equation:

$\frac{dy}{dx} = \frac{y^2 + xy \left(1 + e^{x/y}\right)}{x^2 \left(1 + e^{x/y}\right)}, \quad y(1) = 1$ This equation also appears to be nonlinear and involves exponential terms. A suitable substitution (possibly $u = x/y$) might simplify it.

3. Differential Equation:

$y' = \frac{3y - 7x - 3}{3x - 7y + 7}$ This appears to be another nonlinear first-order equation. Simplification through substitutions or rearranging terms may help in solving.

Would you like me to start with all three or focus on one specific equation first?