Finding derivatives for second order differential equation

[Thoreau123]

Homework Statement

Hello,

My first post here

I have a numerical problem for Matlab but I get stuck with the basic math...

For a circuit I have three equations:

1.Inductance: L=Lo/(1+I^2)
2.Voltage over the inductance: V=L*dI/dt
3.Current over a condensator: I=-C*dV/dt

Homework Equations

From this I should be able to derive the second order differential equation:

4. d2/dt2=2I(dI/dt)^2/(1+I^2)-I(1+I^2)/Lo*C

I know I must find the derivative for V, dV/dt and substitute this into I=-C*dV/dt and this should yield equation 4 but I think my derivatives are all wrong!

The Attempt at a Solution

Basically I need help to use the chain rule (i guess?) and finding the derivative for V=L*dI/dt

This is what I got: dV/dt=dI/dt*(-Lo*2I)/(1+I^2)^2+L*d2/dt2*? something is wrong...

Would really appreciate the help!

 

[Mark44]

Homework Statement

Hello,

My first post here

I have a numerical problem for Matlab but I get stuck with the basic math...

For a circuit I have three equations:

1.Inductance: L=Lo/(1+I^2)
2.Voltage over the inductance: V=L*dI/dt
3.Current over a condensator: I=-C*dV/dt

That's condenser, not condensator. Condensers are usually called capacitors nowadays.

Homework Equations

From this I should be able to derive the second order differential equation:

4. d2/dt2=2I(dI/dt)^2/(1+I^2)-I(1+I^2)/Lo*C

I know I must find the derivative for V, dV/dt and substitute this into I=-C*dV/dt and this should yield equation 4 but I think my derivatives are all wrong!

The Attempt at a Solution

Basically I need help to use the chain rule (i guess?) and finding the derivative for V=L*dI/dt

This is what I got: dV/dt=dI/dt*(-Lo*2I)/(1+I^2)^2+L*d2/dt2*? something is wrong...

Would really appreciate the help!