Math Help - Differential equations

1. Differential equations

I'm struggling with an assignment question.

Solve each of the following differential equations to find the corresponding growth function. (show all necessary calculus)

i. dQ/dt=kt where k>0 t>= 0 Q(0)= Qo

ii. dy/dt=a(q-y) where t>=0 y(0)=0, a and q are constants with a>0, q>0

2. Originally Posted by phillipvdw2001
I'm struggling with an assignment question.

Solve each of the following differential equations to find the corresponding growth function. (show all necessary calculus)

i. dQ/dt=kt where k>0 t>= 0 Q(0)= Qo
$\frac{dQ}{dt}= k~t$

This is of variables seperable type so:

$
\int dQ = \int k~ t~ dt + C
$

where $C$ is determined from your initial conditions

RonL

3. Originally Posted by phillipvdw2001
ii. dy/dt=a(q-y) where t>=0 y(0)=0, a and q are constants with a>0, q>0
Again variables seperable:

$\frac{dy}{dt}=a(q-y)$

so:

$\frac{1}{a(q-y)}~\frac{dy}{dt}=1$

and so:

$
\int \frac{1}{a(q-y)}~dy = \int dt +C
$

Again determine $C$ from the initial conditions

RonL

4. For solution see the attachment