Question 1
If sec(x) dy = dx⁄y and y(π⁄2) = 0, find an equation for y in terms of x.
- y = √ 2sin(x) – 2
- y = √ 2sin(x)
- y = √ 2sin(x) + 2
- y = √ sin(x) – 2
- y = √ sin(x)
Explanation: To solve a separable differential equation, put all the terms with y on one side and all the terms with x on the other side. When you do, you find that y dy = cos(x)dx. Integrating both sides gives 1⁄2y2 = sin(x) + C. Solving for y, y = √ 2sin(x) +2C . Because we know that y(π⁄2) = 0, C must equal –1. So y = √ 2sin(x) – 2 .