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How I can solve this? The impulse response of Vc is wanted.

schematic

I have problem with current in right mesh and I can't write it by Vc or ... . Here is my attempt:

my attempt

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It seems that you have too many currents.

Replaying currents ...

i1, i2 are the currents into meshes (left, right) .
Seems that your equations are "ok" ... but difficult to "read" ...

Here is a Maple sheet with the 3 basic equations (Laplace functions) and solutions.

enter image description here

I have also made a circuit simulation with microcap v12.

enter image description here

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