I need help solving all of these differential equations problems.

1. Consider the linear system dY/dt = AY + f(t), where

Y = (x)

(y) and

1) A = (4 -3), f(t) = ( 2sin(t) )

(6 -7) (sin(t) -cos(t))

2) A = (0 -3), f(t) = ( Exp(10t) )

(3 0) ( -Exp(10t))

3) A = (4 -3), f(t) = (5)

(3 4) (2)

(a) Find the general solution for the system,

(b) Solve the initial value problem Y(0) = (1)

(0)

2. Find the general solution of the system

dx_1/dt = x_2, dx_2/dt = x_3, dx_3/dt = 2x_1 - 2x_2 + x_3

3. Find type and sketch graph of equilibrium point O(0,0) of equation x' = Ax, if

(a) A = (-1 4)

(-4 -1),

(b) A = (-1 4)

(4 0)

1. Consider the linear system-AY + fit), where Y = dY dt and 4 (1)A=(4-3 -jl, fit) =|sin(t)-cos(t) 2 sin( 1) 6 -7 0 -3 3 0 (2) A =| 3 Expo) Exp(10r)) 4 -3 (3)" A= f(t)= 34), (a) Find the general solution of the system, (b) Solve initial value problem Y(0) = 0 2. Find the general solution of the system dx1 dx2 dt dx3 X dt 3. Find type and sketch graph of equilibrium point 0(0,0) of equation x' = Ax, if -1 A=(- ), (b)* A=(-1 A=( 4 4 (b)* (a, 4 -1