Answer:
K= 11
Step-by-step explanation:
You solve for K by subtracting 14 by 25.
25-14= 11
When k is pluged into k 11 the statement is true because it is equal to 11.
When plugged into k+1425;
11+14 =25.
That statement is also true because 25 is equel to 25.
Answer:
Step-by-step explanation:
The problem is very simple, since they give us the solution from the start. However I will show you how they came to that solution:
A differential equation of the form:
Will have a characteristic equation of the form:
Where solutions are the roots from which the general solution can be found.
For real roots the solution is given by:
For real repeated roots the solution is given by:
For complex roots the solution is given by:
Where:
Let's find the solution for using the previous information:
The characteristic equation is:
So, the roots are given by:
Therefore, the solution is:
As you can see, is the same solution provided by the problem.
Moving on, let's find the derivative of in order to find the constants
and
:
Evaluating the initial conditions:
And
Now we have found the value of the constants, the solution of the second-order IVP is: