Separable Equations: Answer to Example 2

Example: Solve the initial value problem

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Answer: This is a separable equation. Indeed, we have

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Before we get into integration we need to look for the constant solutions. These are the roots of the equation tex2html_wrap_inline42 . Since this equation has no real roots, we conclude that no-constant solution exists. Therefore, we proceed with the separation of the two variables and integration. We have

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which gives

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Since

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and

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we get

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The initial condition y(0)=1 gives

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The particular solution to the initial value problem is

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or in the explicit form

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