# Thread: frist order differential equation problem

1. ## frist order differential equation problem

hi there i havent used differential equations for a while now and i have come across a problem which includes:

dN2/dt=B*p(w)(N1-N2)-(1/h)*N2

i tried the seperable method but failed then i put it in wolfram alpha and got a solution and i dont know how wolfram alpha solved it please help

2. ## Re: frist order differential equation problem

Originally Posted by zak9000
hi there i havent used differential equations for a while now and i have come across a problem which includes:

dN2/dt=B*p(w)(N1-N2)-(1/h)*N2

i tried the seperable method but failed then i put it in wolfram alpha and got a solution and i dont know how wolfram alpha solved it please help
This is an odd looking DE. Is p(w) meant to represent p as a function of w, or p times w? Is $\displaystyle \displaystyle N_1$ a constant or a variable? If it's a variable, is it related to $\displaystyle \displaystyle N_2$?

3. ## Re: frist order differential equation problem

yes p represents the energy density and is a function of w. N1 is a variable but since the differential equation is only after the change in N2 i assume that N1 will be a constant

4. ## Re: frist order differential equation problem

Originally Posted by zak9000
yes p represents the energy density and is a function of w. N1 is a variable but since the differential equation is only after the change in N2 i assume that N1 will be a constant
What is w? Is it time dependent? Is N_1 time dependent? ...

I assume B and h are constants

CB

5. ## Re: frist order differential equation problem

Originally Posted by zak9000
hi there i havent used differential equations for a while now and i have come across a problem which includes:

dN2/dt=B*p(w)(N1-N2)-(1/h)*N2

i tried the seperable method but failed then i put it in wolfram alpha and got a solution and i dont know how wolfram alpha solved it please help
Setting $\displaystyle B\ p(w)\ N_{1}=a$ and $\displaystyle B\ P(w)+\frac{1}{h}= b$ and supposing that neither a nor b depend from t the DE is...

$\displaystyle \frac{d N_{2}}{d t} = a - b\ N_{2}$ (1)

... where of course the variables are separable, so that is...

$\displaystyle \frac{d N_{2}}{a-b\ N_{2}}= dt$ (2)

Kind regards

$\displaystyle \chi$ $\displaystyle \sigma$

6. ## Re: frist order differential equation problem

i put the equation into wolfram alpha where x=N2,K=N1
dx/dt=B*K-B*x-x/L

and i got the answer as:
x(t) = c_1 e^((t (-B L-1))/L)+(B K L)/(B L+1)

i was wondering how did it solve to get this answer?