Homework Help: Eliminating a variable from system of ODE's

1. May 10, 2010

gabriels-horn

1. The problem statement, all variables and given/known data

The writing below the equation is the correct order of the constants directly above it.

3. The attempt at a solution

$$h=\frac{-g\prime-a_1g+E(t)}{a_2}$$

So I solved for h in the dg/dt equation, and plug this into the h in the dh/dt equation. My question is where do I go from here to satisfy the relation given in the problem above.

Last edited: May 10, 2010
2. May 10, 2010

vela

Staff Emeritus
Now you want to differentiate your expression for h and plug that result into the LHS of the dh/dt equation to get everything in terms of g and its derivatives.

3. May 11, 2010

gabriels-horn

So $$h=\frac{-g\prime-a_1g+E(t)}{a_2}$$

becomes

$$h\prime=-g\prime\prime-g\prime+E\prime(t)$$

which replaces dh/dt in the original equation?

4. May 11, 2010

vela

Staff Emeritus
You made a few mistakes. What happened to a1 and a2?

5. May 11, 2010

gabriels-horn

sorry, still trying to get used to latex

$$h\prime=\frac{-g\prime\prime-a_1g\prime+E\prime(t)}{a_2}$$

So this result replaces the left hand side of the dh/dt equation in the original system.

Also, dg/dt from the original equation $$dg/dt=-a_1g-a_2h+E(t)$$
becomes

$$g\prime\prime=-a_1g\prime-a_2h\prime+E\prime$$

and plug in dh/dt into this equation, making

$$g\prime\prime=-a_1g\prime-a_2(-a_3g+a_4h)+E\prime$$

Last edited: May 11, 2010