Question

If \[ (7 + e^{2x}) dy - (1 + 2e^{2x})(y + 3) dx = 0, \quad y(0) = 5, \] then \( y(n2) = \)?

Hint:

When solving separable differential equations, first separate the variables, then integrate both sides. Use initial conditions to solve for constants of integration.

Answer 1

This is a separable differential equation. 
To solve it: 
1. Rearrange the equation to separate variables. 
2. Integrate both sides. 
3. Use the initial condition \( y(0) = 5 \) to find the constant of integration. 
4. Solve for \( y(n2) \). After performing the integration, you can find the value of \( y(n2) \).