Ordinary Differential Equations: Separation of Variables: Example 6

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Solve , where y(0) = 1 .

Rewrite the equation in differential form.

Are the variables separated?

Yes.

Do the integration.

We get

How can we determine the constant C?

We can use the initial condition, y(0) = 1.

Set this up.

Substitute.

We get

Solve for C.

Combine these results.

We get

How can we check this result?

We can differentiate it implicitly and compare with the original problem.

Do that.

We get

Solve for

We get , which checks.

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