Numerical solution of differential equations (Euler method)

Hello. I'm having problems with solving a pretty straight forward differential equation by using Euler's method.

Exercise 1: Solve where .

**Answer 1:** This exercise is not the problem (I think). Anyway, the answer is:

.

**Exercise 2:** Solve the differential equation numerically on the interval [0,0.6] with Euler's method using 6 steps.

**Answer 2:** I have tried to use where , but it doesn't make any sense. The "exact" values for x'(t) are

etc.

When I use "my method" the numbers are totally different from them above. Can anyone explain what I do wrong? I must have misunderstand something...