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 3x=14

A:

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 xdy – ydx = x²y³dx

A:

Q: Solve Vr + 5+1 = x

A:

Q: 40 •c 4X-12

A: We know that, The lengths of tangents drawn from an external point to a circle are equal. TP¯=TQ¯

Q: Solve 3*+1=9*=27

A:

Q: Solve  7x - 5 = 8x + 9

A: The equation is given by 7x-5 = 8x+9 To evaluate: The value of x which satisfy the equation.

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: 5 . Solve: x - 3 21

A: We have to solve the equation: 5x-3≥1 Subtracting both sides 1, we get…

Q: Solve 6x - 5 66x

A: Given: 6x-566x

Q: 42

A: We have to solve given equation for y.

Q: P + = 1

A: Consider the function as f(p,q)=p+q-1 then obtain the complete integral for the given function.

Q: Solve 3sin²x - 5tanx = 4

A: Given 3sin2x-5tanx=4

Q: V8x -23 + 18 = 25

A:

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

A:

Q: 3 1 2 42x2у3 1 1 5 83х 3уз

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…

Q: Ive 5x + - Im 3 = 2x -

A: We are asked to solve the equation