How can I solve the differential equations in part B of my homework?

[Radenem]

Homework Statement

I'm not sure how to solve the differential equations for part B.

Homework Equations

Given in Part A of the problem.

The Attempt at a Solution

I attempted to transform the equations in a system with constant coefficients but I'm not sure whether or not this is correct. I can't seem to be able to show what the question is asking!

 

[mark726]

Dear student,

Solving differential equations can be a challenging task, but with the right approach, it can be manageable. In order to solve the differential equations in part B, you can follow these steps:

1. Start by rewriting the equations in a standard form. This means isolating the highest derivative term on one side and all other terms on the other side.

2. Once you have the equations in standard form, you can transform them into a system of equations by letting y1 = y and y2 = y'.

3. Now, you can rewrite the equations in terms of y1 and y2. This will give you a system of two equations with two unknowns.

4. Next, you can solve this system of equations using any method of your choice, such as substitution or elimination.

5. Once you have the values for y1 and y2, you can use them to find the general solution for y.

6. To show what the question is asking, you can plug in the given initial conditions into the general solution to find the specific solution for y.

I hope this helps guide you in solving the differential equations in part B. If you have any further questions or need clarification, please don't hesitate to ask. Remember, practice makes perfect, so keep practicing and you will become more comfortable with solving differential equations. Good luck!