Question

if dy/dx=4y and y=4 when x=0, then y=
a)4e^4x
b)e^4x
c)3+e^4x
d)4+e^4x
e)2x^2+4

Answer 1

\[\frac{dy}{dx}=4y\]
It can be written as
\[\frac{dy}{y}=4dx\]
Now integrate both sides
\[\int \frac{dy}{y}=\int 4 dx\]
Can you do this ?

Answer 2

d.

Answer 3

How did you get this?

Answer 4

i got \[\int\limits_{?}^{?}1/y* dy= 4x+c\]

Answer 5

then ln(y)=4x+c
ln(4)=4(0)+c
ln4=c

Answer 6

Doing great:)

Answer 7

then e^ln(y)=e^(4x+ln4)

Answer 8

y=e^4x+e^lne
=e^4x+4

Answer 9

opps, y=e^4x+e^ln4

Answer 10

Just one mistake
\[\large e^{\ln y}=e^{4x+\ln 4}\]
When two same number with different powers are multiplied, powers add so
\[\large y= e^{4x}\times e^{\ln 4}\]
\[\large y=4e^4x\]

Answer 11

but the e and ln cancel, dont they?

Answer 12

Yeah they cancel

Answer 13

\[\huge e^{\ln 4}=4\]

Answer 14

Do you understand? this is also like that
\[2^{x+y}=2^x \times 2^{y}\]

Answer 15

not really...

Answer 16

Where you have doubt?
\[\large e^{4x+\ln 4}= e^{4x} \times e^{\ln 4}\]
Do you get this?

Answer 17

my teacher taught me to break it up, distribute the e through

Answer 18

ohh and when i do that change the sign to multiplication

Answer 19

Yeah , it changes to multiplication just like
\[2^4=2^{2+2}=2^2 \times 2^2\]

Answer 20

ohh okay. got it. thanks for your patience

Answer 21

No worries:D
Glad to help:P