Linear Equations: Answer to Example 3

Example: Find the solution to

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Answer: This is a linear equation. First we have to rewrite the equation with no function in front of y'. We get

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which may also be rewritten as

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Hence, the integrating factor is given by

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Therefore, the general solution can be obtained as

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Since we have

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we get

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The initial condition tex2html_wrap_inline64 implies

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which gives C=-1. Therefore, the particular solution to the initial value problem is

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