Question 1

All the questions will consider the differential equation given by

$$\ddot x 5\dot x 6x = 2e^{-t}.$$

What is the solution that satisfies $$x(0)=0$$ and $$\dot x(0)=0$$?

Question 2

All the questions will consider the differential equation given by

$$\ddot x 5\dot x 6x = 2e^{-t}.$$

What is the solution that satisfies $$x(0)=1$$ and $$\dot x(0)=0$$?

Question 3

All the questions will consider the differential equation given by

$$\ddot x 5\dot x 6x = 2e^{-t}.$$

What is the solution that satisfies $$x(0)=0$$ and $$\dot x(0)=1$$?