Hi, may I ask, I have y'+(x^n)y=0. Given x=1, ln(y)=-1/4 and x=2, ln(y)=-4. I need to find n. May I know when we perform variable separable on DE, do we include constant C?

Question

kc_kennylau · Answer

what's DE?

anonymous · Answer

Differential equation?

abb0t · Answer

If you weren't given initial conditions, you do need to include C. But "C" is just a constant.

abb0t · Answer

But, if I am reading your question correctly, you do have initial conditions, so you do need to solve for constant, C.

anonymous · Answer

I know, but the problem is, I do not know n so how can I solve C?

kc_kennylau · Answer

Use the initial conditions

kc_kennylau · Answer

One for solving n and one for solving c

anonymous · Answer

oh? we are gonna use it separately? but i actually thought of doing it simultaneous equation way, and cancel out C in order to find n but I was stuck half way

anonymous · Answer

use the initial condition

kc_kennylau · Answer

Bear in mind that x=1, ln(y)=-1/4 is ONE condition

anonymous · Answer

Yes, that is true, but then the way to solve is it integrate differential eq and then substitute the conditions in it to get 1st eq right? Then i think we will end up with n and C. Do we do the same and get a 2nd equation using the 2nd condition then do simultaneous eq?

anonymous · Answer

$$-\ln |y|= \frac{ x^{n+1} }{ n+1 }+C$$

anonymous · Answer

the above eq is what i got from the integration of Diff Eq. So, is it right?