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. .----------. v= i x R . | ^ | . | | | d 3 . +| | | and i= - -- (3 x v ) . --- / dt . C --- v \\ R . | / 2 dv . | | \\ so v = -9 x R x v x -- . | | | dt . | | | . '----------. . . . 2 dv dv . this becomes v + 9 x R x v x -- = v x ( 1 + 9 x R x v x -- )=0 . dt dt . . at each instant of time because although C is nonlinear the basic . . . laws of physics still apply to the circuit. . . . The above equation has only two possible solutions: . . . 1) v(t)=0 for all t, which is ruled out because we need v(0)=1 . . -------------- . | 2 . 2) v(t)= | 1 - ----- x t . \\| 9 x R . . . . 9 x R dv . at time t= ----- v=0, the v x ( 1 + 9 x R x v x -- )=0 . 2 dt . . 9 x R . equation still applies where t is now measured from ----- . 2 . . and since v(0)=0 the v(t)=0 solution does . . dv . apply, and the 1 + 9 x R x v x -- = 0 solution leads to an . dt . . an imaginary and extraneous result. . . . All of this can be condensed into: . . . . ---------------------- . | 2 . v(t)= | MAX(0,1 - ----- x t) t>=0 . \\| 9 x R . .