Question

Differential equation help. *Question attached below* Will give medal.

Answer 1

Can someone walk me through this question step by step, please?

Answer 2

start by multiplying \(\large e^{\alpha t}\) through out

Answer 3

Okay, let me try that

Answer 4

Hmm, I understand that is the integrating factor, but how did you end up with \[e ^{alphat}\]

Answer 5

Oh nevermind, I understand why that

Answer 6

derivation for integrating factor method is pretty interesting, we can work it from scratch if you're interested.. but we normally use the IF formula directly :

for equation of form \(\large y' + p(t) y = q(t)\), the integrating factor is given by
\[\large IF = e^{\int p(t) ~dt}\]

Answer 7

Hmm, I'm now stuck at
\[ve ^{\alpha t}= \int\limits_{}^{}e ^{\beta t}e ^{\alpha t}\]

Answer 8

il give a hint
\[\large x^m\cdot x^n = x^{m+n}\]

Answer 9

RHS = \[e ^{t(\alpha + \beta)} \]

Answer 10

rhs=medeal+boop+yhahahhahahahahahahha=:DD

Answer 11

@iTiaax how are you doing on this?

Answer 12

@freckles , I think I just figured it out.

Answer 13

congrats!

Answer 14

Thank you :)