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## Homework Statement

Obtain [itex]i_1[/itex] and [itex]i_2[/itex] for t > 0 in the circuit below.

http://img258.imageshack.us/img258/7765/problem60as1.jpg [Broken]

## Homework Equations

[tex]V_L\,=\,\frac{di_L}{dt}[/tex]

## The Attempt at a Solution

To get initial conditions, I made a second circuit diagram for t < 0.

http://img219.imageshack.us/img219/8606/problem60part2ch2.jpg [Broken]

Since there is no current before t = 0, both initial currents and voltages are zero.

[tex]i_1(0^-)\,=\,i_1(0^+)\,=\,0\,A[/tex]

[tex]i_2(0^-)\,=\,i_2(0^+)\,=\,0\,A[/tex]

[tex]V_1(0^-)\,=\,V_2(0^-)\,=\,0\,V[/tex]

I also made a third circuit diagram for t > 0.

http://img254.imageshack.us/img254/2797/problem60part3ii5.jpg [Broken]

[tex]i_1\,=\,\frac{di_1}{dt}[/tex]

[tex]i_2\,=\,\frac{V_1\,-\,V_2}{3\Omega}[/tex]

[tex]i_3\,=\,\frac{0\,-\,V_1}{2\Omega}[/tex]

KCL @ [itex]V_1[/itex]:

[tex]4\,A\,+\,i_3\,=\,i_1\,+\,i_2[/tex]

[tex]4\,-\,\frac{V_1}{2}\,=\,\frac{di_1}{dt}\,+\,\frac{V_1\,-\,V_2}{3}[/tex]

KCL @ [itex]V_2[/itex]:

[tex]\frac{V_1\,-\,V_2}{3}\,=\,\frac{di_2}{dt}[/tex]

Here I am stuck, I know that I need to produce a second order differential equation before I can even think about solving this circuit, but I am having trouble finding what equations to use to get such an O.D.E. Please help!

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