Question

The particular solution of the differential equation dy dt equals y over 4 for which y(0) = 20 is

a. y = 20e−0.25t
b. y = 19 + e0.25t
c. y = 20 e0.25t
d. y = 20e4t

Answer 1

@across

Answer 2

Hello @across

Answer 3

Can you help @ganeshie8

Answer 4

familiar with separation of variables ?

Answer 5

No I just learned this subject today and I am not quite understanding it.

Answer 6

may i suggest you watch this awesome video quick
https://www.khanacademy.org/math/differential-equations/first-order-differential-equations/separable-equations/v/separable-differential-equations-introduction

Answer 7

Okay.

Answer 8

Okay so that kindof cleared it up for me but I am still a little bit fuzzy in some places.

Answer 9

They key thing here is to get get x terms and dx on one side
y terms and dy on the other side

Answer 10

x is t in our case

Answer 11

Okay I got that part. What would be my first step in solving the problem?

Answer 12

Could you show me what you get after separating ?

Answer 13

\[\frac{ dy }{ dt }= \frac{ y }{ 4 } \]
after separated
\[ydy=4dt\]
Is that correct?

Answer 14

Nope, but its a good try. Try again...

Answer 15

What am I doing wrong? because in the video he multiplied both sides with y and dy or in this case dt

Answer 16

The goal is to get dy and y terms on one side

Answer 17

Ohh not on opposite sides like in the video?

Answer 18

give it a try

Answer 19

ydydt=4

Answer 20

I mean ydy-dt=4

Answer 21

Heyy its just algebra :

\[\frac{ dy }{ dt }= \frac{ y }{ 4 }\]

divide \(y\) both sides and get
\[\dfrac{1}{y}\dfrac{dy}{dt} = \dfrac{1}{4}\]

multiply \(dt\) both sides and get
\[\dfrac{1}{y}dy = \dfrac{1}{4}dt\]

Answer 22

Okay why do you have the 1 over the y and the 4?

Answer 23

that is a good question

Answer 24

I thought you said that we should have the dy and y terms on one side?

Answer 25

Can you please show me the steps and walk me through them so I can understand how to do the problem?

Answer 26

Consider below equation :

\[x=2y\]

Answer 27

Okay

Answer 28

divide \(2\) both sides, what do you get ?

Answer 29

\[\frac{ dy }{ dx }=\frac{ 1 }{ 2 }\]
\[\frac{ dx }{ dy }=2\]

Answer 30

@mathmale @across @jim_thompson5910 @retirEEd

Answer 31

\[\ln y=\frac14x+c\\y=ce^{\frac x4}\\20=c\\y=20e^{\frac x4}\]

Answer 32

so is that C or D? @across

Answer 33

dy dt equals y over 4:\[\frac{ dy }{ dt}=\frac{ y }{ 4 }\]...after cross-mult., becomes (dy/y)=(dt/4), or (dy/y)=(1/4)dt.

Answer 34

Thank you I got it correct.

Answer 35

Glad you got it right! Sorry not to have responded earlier.

Answer 36

Any loose ends to tie up? or are you all clear on this problem now?