# Convert the Second Order Equation

• Feb 11th 2010, 07:45 AM
Len
Convert the Second Order Equation
Convert the second order equation

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

into a first order system using:

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

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

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I'm not really sure with this but

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

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

Then I have no idea. Some help would be very appreciated.
• Feb 11th 2010, 07:52 AM
Calculus26
you are correct in that dv/dt = 0

v = k1

Then

v = dy/dt = k1

y = k1 *t + k2
• Feb 11th 2010, 07:52 AM
dedust
Quote:

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

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

the solution is $v(t) = C_1$

Quote:

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

$~dy = C_1 ~dt$

$y(t) = C_1t + C_2$