# Thread: Solution of a simple Differential Equation

1. ## Solution of a simple Differential Equation

Hi,

I was wondering if anyone could help me solve or even know the type of the differential equation below

$d^2x/dt^2= k.dy/dt$

where k is a constant.

Thanks very much

Gareth

2. Originally Posted by gabrown
Hi,

I was wondering if anyone could help me solve or even know the type of the differential equation below

$d^2x/dt^2= k.dy/dt$

where k is a constant.

Thanks very much

Gareth
$\frac{d^2x}{dt^2} = k~\frac{dy}{dt}$

So
$\int \frac{d^2x}{dt^2}~dt = k \int \frac{dy}{dt}~dt$

$\frac{dx}{dt} = ky + C$

This is as far as we can go unless you want to put the solution in integral form:
$\int \frac{dx}{dt}~dt = k \int y(t)~dt + Ct$

$x(t) = k \int y(t)~dt + Ct + A$

-Dan

3. Originally Posted by topsquark
$\frac{d^2x}{dt^2} = k~\frac{dy}{dt}$

So
$\int \frac{d^2x}{dt^2}~dt = k \int \frac{dy}{dt}~dt$

$\frac{dx}{dt} = ky + C$

This is as far as we can go unless you want to put the solution in integral form:
$\int \frac{dx}{dt}~dt = k \int y(t)~dt + Ct$

$x(t) = k \int y(t)~dt + Ct + A$

-Dan

so if we have

$d^2y/dt^2= -k.dx/dt$

as well can we come up with a way of putting x and y as just functions of t?