Question

Find the particular solution y=f(x) to the given differential equation with the initial condition f(0)=-2
dy/dx=e^x+4x/y

Answer 1

Is the right side \(\dfrac{e^x+4x}{y}\), or \(e^x+\dfrac{4x}{y}\) ?

Answer 2

\[\frac{ dy }{ dx}=\frac{ e^x+4 }{y }\]

Answer 3

Oh, much easier. It's separable, so you can split the differentials:
\[y~dy=(e^x+4)~dx\]

Answer 4

Integrate both sides, then make use of the initial condition. Solve for \(y\) if you like

Answer 5

Great work, Siths! But please involve @sarcos11 towards finding his/her own solution. I'm sure he/she can do some of this work unaided. Thank you.

Answer 6

No problem! I have trouble staying my hand most of the time :)

Answer 7

I'm a girl.

Answer 8

my teacher taught me that we are suppose to use u
ex.
u=y
du/dy=1
dy=du/1
is this necessary for this problem

Answer 9

do you mean

\[\frac{ dy }{ dx}=\frac{ e^x+4x }{y }\]?

Answer 10

You asked, " u=y
du/dy=1
dy=du/1
is this necessary for this problem"

I'd agree with sarcos11: no.
\[\frac{ dy }{ dx}=\frac{ e^x+4 }{y }\] is very easily separable, as sarcos11 has already pointed out. Separate the equation by variables, and then integrate each side separately.

Answer 11

i'm sorry i meant to say yes

Answer 12

I am so confused right now