# Need help simplifying equation to find the laplace transform of it

there are two loops in an electrical circuit. ive got two equations and two unknowns.
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.

Tom Mattson
Staff Emeritus