Differential Equations

4. Use Gauss-Jordan elimination to transform the augmented matrix of the following system to RREF. Then use the Nonhomoge- neous Principle to write the solution of the linear system in the form X = X₁ + Xp- vrie 2x1 22 23 2 4x1 + x2 + 5x3 = 4 x1 + x2 + 2x3 = 1 Bo

20. Find the general solution of the following differential equation. y' = x² + x²y

4) Determine whether the following systems are causal: (a) y(t) = x(-t) and (b) y(t) = x(t+1)

5) Determine whether the following systems are invertible: (a) y(t) = x(-t) and (b) y(t) = tx(t)

6) Determine whether the following systems are BIBO-stable: (a) y(t) = x²(t) and (b) y(t) = tx(t)

2) Determine the time invariance of the following systems: (a) y(t)=x(t)u(t)

1. Use Cramer's rule to solve the following system Algebraic equations: X-Y +2Z=-5 -X+3Z=0 X+Y=1

1) Show that the system described by the equation is linear dy(t) dt - +3y(t) = x(t)

Determine the 'utions for the following equations: 1). 2) 3). 0:1 م (x *(x² + y 2) + y) dx + (y *(x² + y²) + x) dy=0 2 (x y + x) y'=y y' + y/(1-x) = x²

Determine a complete solution of the following equations: 1. y" y' + y = 0 where y (0)=1, and y' (0) = 0 2. 9 y" + 16 y = 32 - 50 e 2x 3. y" + 9 y' = 10 cos 3x 5:19 م