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here are the equations

v(t) = I1*R1 + 1/c*int(I1*dt) - 1/c*int(I2*dt) - first loop

0 = LdI2/dt + R2*I2 - 1/c*int(I1*dt) + 1/c*int(I2*dt) - second loop

the capacitor is in the branch between the two loops.

Im drawing a blank on this. I need to simplify into one equation so I can find the laplace transform of the one equation.

the goal is to find the step response of the system using matlab.