1. Worked Out Answer 4.4.3 4 From: Maths in Motion – Theo de Haan

2. First, classify the DE: You are looking for a solution z(t) first - Nonlinear because of square - Order: 1 Highest derivative of this function:

3. - Nonlineair - Order: 1 Strategy: Separation of variables First, classify the DE:

6. All terms containing z to the left side. All terms containing t to the right side.

7. You may now integrate both sides.

8. Rewrite the expression on the left side and determine the integrals.

9. One integration constant: the sum of the one on the left side and the one on the right side.

10. Because you divide everything by 2, also the constant will change. Hence the prime.

11. Do not forget the double product while squaring.

12. So, the general solution of the DE: equals: You can easily check this: Determine the derivative of z(t)… Indeed, the right side equals z. and square it…

13. z(t) is a position function. Boundary condition: z(0) = 0 So: Given the boundary condition, the position function is: