Question

Use the elimination method to find a general solution for the given linear​ system, where differentiation is with respect to t.

(D+1)[u]−(D+1)[v] = eᵗ
(D−1)[u]+(3D+1)[v] = 7

Answer 1

you must ask the given Lena's system d + 1 you - d + 1 = 7 so I got the same thing to do so minus 7277 / 1 = 3 days + 734 is every 3 days 87 if you make it 3 Days every 3 days and you're going to eat we can you please e and then plus d + 1 and 1 + 1 - 1 the d plus d plus d minus 1 bye thank you

Step-by-step explanation:

so so add d plus one you plus that one then it gets the answer 7 and congratulations

Answer 2

To find the general solution using the elimination method, we will eliminate one of the variables by manipulating the equations. Step-by-step, we multiply the equations by appropriate factors, simplify them, add them together, simplify further, and set the equation to zero to obtain the general solution.

Step-by-step explanation:

The given linear system is:

(D+1)[u] - (D+1)[v] = e^t(D-1)[u] + (3D+1)[v] = 7

To find the general solution using the elimination method, we will eliminate one of the variables by manipulating the equations.

Step 1: Multiply the first equation by (D-1) and the second equation by 1.

((D+1)(D-1))[u] - ((D+1)(D-1))[v] = (D-1)e^t(D-1)[u] + (3D+1)(D-1)[v] = 7(D-1)

Step 2: Simplify the equations.

(D^2 - 1)[u] - (D^2 - 1)[v] = (D-1)e^t(D-1)[u] + (3D^2 - 1)[v] = 7(D-1)

Step 3: Add the equations together.

(D^2 - 1)[u] - (D^2 - 1)[v] + (D-1)e^t(D-1)[u] + (3D^2 - 1)[v] = 7(D-1)

Step 4: Simplify and rearrange the equation.

((D^2 - 1) + (D-1)e^t(D-1))[u] + ((3D^2 - 1) - (D^2 - 1))[v] = 7(D-1)

Step 5: Simplify further.

(D^2 - 1 + (D-1)e^t(D-1))[u] + (2D^2)[v] = 7(D-1)

Step 6: Set the equation to 0.

(D^2 - 1 + (D-1)e^t(D-1))[u] + (2D^2)[v] - 7(D-1) = 0

This is the general solution for the given linear system using the elimination method.