The state equation for the current I1 shown in the network

The state equation for the current I₁ shown in the network given below in terms of the voltage V_x and the independent source V, is given by

Using KVL in loop (1), we get

V = 3(I₁ + I₂) + V_x + 0.5	dI₁	........(1)
	dt

and using KVL in loop (2), we have

and 0.5	dI₁	= 5I₂ - 0.2V_x .......(2)
	dt

Solving (1) and (2),

	dI₁	=	5	V -	15	I₁ - 1.4V_x
	dt		4		4

	dI₁	= -1.4V_x - 3.75I₁ +	5	V
	dt		4

	dI₁	= -1.4V_x - 3.75I₁ -	5	V
	dt		4

	dI₁	= -1.4V_x + 3.75I₁ +	5	V
	dt		4

	dI₁	= -1.4V_x + 3.75I₁ -	5	V
	dt		4