the solution to the differential equation dy/dx=10xy with the initial condition y(0)=2 is?

Question

eyust707 · Answer

I believe you can just separate the variables

eyust707 · Answer

then integrate both side

eyust707 · Answer

youll end up with a constant from the integration

anonymous · Answer

would i take out the 10?

eyust707 · Answer

no

eyust707 · Answer

$$(1/y)9 dy = 10x dx$$

anonymous · Answer

oh okay. so the 10 goes with the x? and the answer choices all have ln or e in them

eyust707 · Answer

$$\int\limits (1/y) dy = \int\limits 10xdx$$

eyust707 · Answer

the 10 could go on either side but with the x is much easier

anonymous · Answer

okay so far i have ln y=5x^2

anonymous · Answer

That's correct :)

anonymous · Answer

Should add C, though!

anonymous · Answer

according to the answer choices i have, im done yet lol

anonymous · Answer

You need to find y!

anonymous · Answer

yeah i guess. then i got y=5x^2/ln, which should equal e^5x^2 right?

anonymous · Answer

Yep, still don't forget C

anonymous · Answer

then if i plugged in y(0)=2 i would get e^5x^2?

anonymous · Answer

the answer choices are
A. ln((5x^2)+2)
b.e^5x^2+2
C. e^5x^2+1
D.2 ln(5x^2)
E. 2e^5x^2

anonymous · Answer

What did I keep reminding you ?
The constant C!

anonymous · Answer

ohhh....i got you know. the constant c would be 2. oh wow i feel stupid now

anonymous · Answer

can you help me with another question?

anonymous · Answer

:) So you know the purpose of initial value now!

anonymous · Answer

Just open the new post!

anonymous · Answer

okay i did. and thank you for your assistance with the last problem