Consider the 2 × 2 system of ODEs, where X(t) x₁(t) and x2(t). (x₁(t)\ === for some real-valued functions X'(t) = -²) x(t), x (0) = (7 -2 2 (a) Find the explicit, real-valued solution of this system, both in vector form and in component form. (b) Roughly sketch what you expect the phase portrait of this graph to look like.

Q: Solve                 2   =   X-500/ 85

A: Firstly, we add 500/85 on both sides  and then by adding 2+500/85, we get the required result.

Q: Solve  5x =-5 3

A: Solve  5x =-5 3

Q: solve the equestion y-8/5 +2=2/5-y/3

A: Given:

Q: Solve: a 5X-1 = 7x

A: We have to solve for x.

Q: Solve Vr + 5+1 = x

A:

Q: SOLVE 8-2y=4

A: Given that  8-2y=4               ⇒2y=8-4               ⇒2y=4                ⇒y=2…

Q: Differentiate - 3x 1 X+- X,

A:

Q: Orthonormalize the set {(¿).(9)} with respect to the inner product from before.

A:

Q: V8x -23 + 18 = 25

A:

Q: 7. Solve: 3 = 2 x-1 + 5 x+1

A:

Q: "X" is the opposite side in the figure. Find the opposite side/solve for x..

A:

Q: 3. Solvex+17 = 35

A: Given the equation  x5 + 17 = 35 We need to solve it. Now, x5 + 17 = 35 implies that  x5 = 35 - 17…