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Solve the differential equation (dy/dx)² - (dy/dx)(e^x + e^(-x)) + 1 = 0.
- y = e^x + c
- y = -e^(-x) + c
- y = 2e^x + 3e^(-x) + c
- y e^x + 1 = c e^x
Correct answer: y = e^x + c
Solution
Factoring the quadratic in dy/dx gives dy/dx = e^x or dy/dx = e^-x; integrating the first gives y = e^x + c (one valid family).
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