Final answer:
To solve the initial value problem dy/dx = 3y - 5e^(-2x), you can use separation of variables. Solve for y by integrating both sides with respect to their respective variables.
Step-by-step explanation:
Solution:
To solve the initial value problem dy/dx = 3y - 5e^(-2x), we can use separation of variables. Here are the steps:
1. Rewrite the equation as dy/(3y - 5e^(-2x)) = dx.
2. Integrate both sides with respect to their respective variables.
3. Solve for y by isolating it on one side of the equation.
The detailed solution involves integrating the left side of the equation with respect to y and the right side with respect to x.
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