Linear Equations: Answer to Example 2

Example: Solve the following initial value problem for t > 0

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Answer: This is a linear equation. Let us follow these steps for solving such equations:

1.
We have to divide by 2t

displaymath102

2.
We get the integration factor u(t) by

displaymath106

3.
The general solution is given by

displaymath108.

Since

displaymath110

Therefore, we have

displaymath112

4.
The solution to the given initial value problem may be obtained by using the initial condition y(2)=4. We have

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which gives tex2html_wrap_inline118 . Therefore, the solution is

displaymath120

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Author: Helmut Knaust
Last Update 6-22-98

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