9–61. Evaluate and simplify y'.


y = e^2θ

Verified step by step guidance

1. Identify the given equation: y' * y = e^(2θ). Here, y' represents the derivative of y with respect to θ.
2. Rearrange the equation to isolate y': y' = e^(2θ) / y. This will help us express the derivative in terms of y and θ.
3. Recognize that this is a separable differential equation, allowing us to separate variables: dy/y = e^(2θ) dθ.
4. Integrate both sides: ∫(1/y) dy = ∫e^(2θ) dθ. This will yield the natural logarithm of y on the left and an exponential function on the right.
5. Solve for y by exponentiating both sides after integration, which will give you y in terms of θ, and simplify the expression as needed.