Question

give a formula for the solution y(x) of the differential equation y'(x) = 0.4y(x) with y(0)=8

Answer 1

hmm...a separable differential equation\[ y'(x) = 0.4y(x)\]\[\frac{\text{d}y}{\text{d}x}=0.4y\]\[\frac{\text{d}y}{y}=0.4\ \text{d}x\]

Answer 2

but what is the y(x) function?

Answer 3

i got y(x) =e^(0.4(0.5x^2+20)) but its incorrect

Answer 4

first,did u integrate that? dy/y=0.4x
what did u get? write that

Answer 5

i got y'(x)/0.4y(x) = 1

Answer 6

this is all steps i wrote it, but it still incorrect

Answer 7

this is simpler than u solved,u just need to integrate this on both sides,
\[\frac{dy}{y}=0.4dx\]

Answer 8

someone suggest me write as this ln(y) = 0.4x +c then y(0)=8 will gives me ln(8)0=c. therefore, ln(y)=0.4x+ln(8))

Answer 9

is that the same thing as yours?

Answer 10

after integrating that u WILL get that:
as \[\int\limits_{}^{}dy/y=\ln y\]
and
\[\int\limits_{}^{}0.4dx=0.4x+c\]
so yes,same thing

Answer 11

i got the lny(x) = 2x/5 + 8

Answer 12

but how did u get c as 8?

Answer 13

c is ln(8)

Answer 14

y= e^(2x/5 + ln(8))

Answer 15

now thats correct :)

Answer 16

thank you!

Answer 17

welcome :)

Answer 18

also can you help me on this one?

Answer 19

sure.

Answer 20

i did several times, still incorrect. i got the tips that need use integral by part, u = sinIntegral(x)

Answer 21

this seems difficult for me too,need some time.

Answer 22

i think we don't need take the sinIntegral(x) apart. we could see it as a whole thing?

Answer 23

i have never solved such integral.....this reference gives the integral of sinintegral x:

http://mathworld.wolfram.com/SineIntegral.html

Answer 24

emm ok. thx for taking ur time

Answer 25

i would hand this back to @mukushla