- #1

DaxInvader

1. Homework Statement

1. Homework Statement

We have this initial Equation: d

^{2}y/dt

^{2}−7dy/dt+ky=0, and we need to find the values of k in which the solution y=e

^{3t}applies and the general solution.

## The Attempt at a Solution

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In this case, I simply started to find k but substituting y into the equations.

y(t) = e

^{3t}, y'(t) = 3*e

^{3t}, y''(t) = 9*e

^{3t}

We get: 9e

^{3t}- 7*(3*e

^{3t}) + k*e

^{3t}= 0

=> 9*e

^{3t}-21*e

^{3t}+ k*e

^{3t}= 0

=>e

^{3t}* (k-12) = 0.

I find the value of K in which y = e

^{3t}is a solution to be 12.

Where I am lost is to find the general solution? Do I already have the necessary information?

**[/B]**

## Homework Statement

Find all values of k for which the function y=sin(kt) satisfies the differential equation y′′+11y=0. Hint: There are more than 2 values of k

## The Attempt at a Solution

We know that y is a solution of the DE.

y'(t) = sin(kt), y'(t) = kcos(kt), y''(t)= -k

^{2}sin(kt)

By substitution:

-k

^{2}sin(kt) + 11sin(kt) = 0

=> sin(kt)(11-k

^{2})=0

I find that √11 for k is a solution, 0 is a solution, and any multiple of π is a solution as well. I tried entering the following:

√11, 0, nπ

And It is not correct. Any tips to see if I did something wrong?Thanks for your help!