# Convert the Second Order Equation

• Feb 11th 2010, 06:45 AM
Len
Convert the Second Order Equation
Convert the second order equation

$\displaystyle \frac{d^2y}{dt^2}=0$

into a first order system using:

$\displaystyle v=\frac{dy}{dt}$

Then find the general solution for $\displaystyle \frac{dv}{dt}$ equation then sub the solution into the $\displaystyle \frac{dy}{dt}$ equation and find the solution of the system.

------------

I'm not really sure with this but

$\displaystyle \frac{dy}{dt}=v , \frac{dv}{dt}=0$

so $\displaystyle y(t)=k_1*e^t, v(t)=k_2$

Then I have no idea. Some help would be very appreciated.
• Feb 11th 2010, 06:52 AM
Calculus26
you are correct in that dv/dt = 0

v = k1

Then

v = dy/dt = k1

y = k1 *t + k2
• Feb 11th 2010, 06:52 AM
dedust
Quote:

Originally Posted by Len
Then find the general solution for $\displaystyle \frac{dv}{dt}$ equation

$\displaystyle \frac{dv}{dt} = 0$

the solution is $\displaystyle v(t) = C_1$

Quote:

then sub the solution into the $\displaystyle \frac{dy}{dt}$ equation and find the solution of the system.
$\displaystyle \frac{dy}{dt} = v(t) = C_1$

$\displaystyle ~dy = C_1 ~dt$

$\displaystyle y(t) = C_1t + C_2$