Question:
If
\[
(7 + e^{2x}) dy - (1 + 2e^{2x})(y + 3) dx = 0, \quad y(0) = 5,
\]
then \( y(n2) = \)?
If
\[
(7 + e^{2x}) dy - (1 + 2e^{2x})(y + 3) dx = 0, \quad y(0) = 5,
\]
then \( y(n2) = \)?
Show Hint
When solving separable differential equations, first separate the variables, then integrate both sides. Use initial conditions to solve for constants of integration.
Updated On: Jan 14, 2026
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Solution and Explanation
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 \( y(n2) \).
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