Answer:
Step-by-step explanation:
First you need to rearrange the original equation in order to have an equation with a general form:
We divide everything by D, so we have:
We know that k and D are constants, so we can leave them as just one constant that gives as result:
Then we proceed to change terms in the equation son it looks friendlier:
Knowing that
Then we give the general solution for the differential equation of second order:
The following is knowing the frontier values so we can calculate the constants of the equation:
With these values, we can replace in the general solution to find the final equation:
And with the other values:
Then we solve the equation system, as we have two unknowns, the constants, and two equations:
After solving both equations, we have;
The we see that we can cancel terms, so we have the final solution that is: