- #1

roam

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## Homework Statement

Find a one-parameter family of solutions to the differential equation:

[itex]\frac{dy}{dt} = \frac{t \ cos 2t}{y}[/itex]

Are there any solutions to the differential equation that are missing from the set of solutions you found? Explain.

## The Attempt at a Solution

I used the separation of variables to find the solution as follows:

[itex]\int ydy = \int t \ cos (2t) dt[/itex]

[itex]\frac{y^2}{2} = \frac{1}{4} (2t \ sin (2t)+ cos(2t)) + c[/itex]

[itex]\therefore y = \sqrt{t \ sin (2t)+ \frac{1}{2} \ cos (2t) + k}[/itex]

And this is defined as long as there is no negative under the square root. So, how do I know whether there are any missing solutions or not? And how do I identify them?