Question

Solve the following initial value problem completely, and check your answer by comparing it to the solution using the methods of Chapter 2 or Chapter 3 **+ 4x = 7, x(0) --> X(t) =

Answer 1

To solve the initial value problem x'(t) + 4x = 7 with x(0), substitute the initial conditions into the general solution, solve for constants, and check the solution against the problem's conditions.

Step-by-step explanation:

To solve the given initial value problem x'(t) + 4x = 7, with the initial condition x(0), and find the function X(t), follow these steps:

1. Set up the differential equation and apply the initial condition to find the particular and homogeneous solution.
2. Substitute the values of x and t from the initial condition into the general solution to solve for the constants.
3. Solve the simultaneous equations for the unknowns.

To check the solution, make sure all values satisfy both the initial value problem and any information provided in the problem statement from previous chapters.