Answer:

Step-by-step explanation:
The general solution will be the sum of the complementary solution and the particular solution:

In order to find the complementary solution you need to solve:

Using the characteristic equation, we may have three cases:
Real roots:

Repeated roots:

Complex roots:

Hence:

Solving for
:

Since we got complex roots, the complementary solution will be given by:

Now using undetermined coefficients, the particular solution is of the form:

Note:
was multiplied by x to account for
and
in the complementary solution.
Find the second derivative of
in order to find the constants
and
:

Substitute the particular solution into the differential equation:

Simplifying:

Equate the coefficients of
and
on both sides of the equation:

So:

Substitute the value of the constants into the particular equation:

Therefore, the general solution is:


Answer:
13.38
Step-by-step explanation:
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M = (y2 - y1) / (x2 - x1)
m = (-2 - 2) / (4 - 0)
m = -4 / 4
m = -1
The slope of the line that goes through (0, 2) and (4, -2) is -1.
Answer:
5,004,300
Step-by-step explanation: