[differential equations] help understanding a question

Author Summary

ghostof_IamBeepBeep2 is in differential equations

Post Body

https://i.imgur.com/kn6FiJo.jpg

My understanding is to differentiate the given y function twice which gives me

y''= ab² * e^bx

at this point i substitute y'' and y into a) and i solve for b by diving both sides by ae^bx which would leave me with b² = 4, and ultimately b = 2 and b = -2.

So would the two solutions for a) be y = ae^-2x and y = ae^2x ?

what about the part that asks to prove no other solutions of this form exist. is the work i've done so far enough, or do i need to do more? if so, what else do i need to do?

Author

Account Strength

100%

Account Age

8 years

Verified Email

Yes

Verified Flair

Total Karma

53,258

Link Karma

17,805

Comment Karma

35,305

Profile updated: 4 months ago

Posts updated: 9 months ago

ghostof_IamBeepBeep2

Subreddit

r/learnmath

Post Details

Location

differential equations

We try to extract some basic information from the post title. This is not always successful or accurate, please use your best judgement and compare these values to the post title and body for confirmation.

Posted: 5 years ago
Reddit URL: View post on reddit.com
External URL: reddit.com/r/learnmath/c...