Find an explicit solution of the given initial-value problem. 1. dx/dt = 4(x 2 + 2), x(/4)

Fi­nd an explicit solution of the given initial-value problem.

1. dx/dt = 4(x² + 2), x(π/4) =1

2. dy/dx = (y² - 2)/ (x² - 1), y(2) = 2

3. x² dy/dx = y – xy, y(-1) = -1

4. dy/dt + 2y = 1, y(0) = 5/2

5. √(1 – y²) dx – √(1 – x²) dy = 0, y(0) = √3 / 2

6. √(1 – y⁴) dy + x(1 + 4y²) dx = 0, y(1) = 0