## mathlife 2 years ago find the Differential Equation of the given Family. Y= Ce^(2x) + e^(-2x)

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1. abb0t

Take the first and second derivative of the given solution.

2. abb0t

Then do a little substitution of y...

3. vf321

@mathlife You should really follow abb0t's advice. Do not expect us to give a solution for you.

4. vf321

If it worked out, close the question. If you are still having trouble, let us know.

5. TuringTest

there is a neat way to do it with matrices :)

6. abb0t

I don't think they should expect ANY answers for any math course above Calculus 1.

7. abb0t

@TuringTest HAHAHA i prefer to stay away from that route. Nope. No way.

8. TuringTest

aw, but it's really pretty cool and fast, plus it works for any set of exponents e^ax, e^bx

9. vf321

@TuringTest No need to make things more complicated... you may have to end up explaining matrix operations to OP.

10. abb0t

Can't you use Wronskian too?

11. TuringTest

Don't worry, I wasn't going to post, you abb0t has described enough no, much easier than the wronskian

12. TuringTest

no, because you don't get a square matrix

13. vf321

BTW guys I think @mathlife is leaving out some info - I can think of a first-order DE that satisfies this as well as the double-root second-order linear DE we're all thinking of...