General Contents
Detailed Contents
Index
Linear Differential Equations: Example 1
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Solve the differential equation,
.
General Contents
Detailed Contents
Index
What type of differential equation is this?
It is a first order linear differential equation.
What is the general form of this type of equation?
What is the general solution?
General Solution:
What is
P
(
x
) in this problem?
What is
Q
(
x
) in this problem?
Part of the solution
, looks complicated. How do we determine it?
We can determine the exponent,
separately.
Set up the integral, using
.
.
Do the integral.
We get
.
Use this to
evaluate
Simplify the last expression.
Substitute this result in the General solution above.
becomes
Do the multiplication on the right under the integral sign.
Do the integration.
How do we solve for y?
Divide by
x
2
.
Do it.
How can we check this result?
We can differentiate it and see if it satisfies the original equation.
Do the differentiation.
Substitute this result and our result for y in the left-hand side of the original equation.
We get
Simplify by doing the multiplication and collecting like terms.
We get
Does this check?
Yes, it matches the right-hand side of the original equation.
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