Question

Find the solution to the linear system of differential equations

x = 50x - 72y,
y = 36x - 52y,
satisfying the initial conditions x(0)=-5 and y(0) = -3.

Answer 1

To find the solution to the linear system of differential equations x = 50x - 72y and y = 36x - 52y, you can solve for x and y using substitution. The solution is x = 89728/1803 and y = 0.0496.

Step-by-step explanation:

To find the solution to the linear system of differential equations x = 50x - 72y and y = 36x - 52y, we can solve for x and y using substitution:

First, substitute the value of x in the second equation:

y = 36(50x - 72y) - 52y

Simplify the equation:

y = 1800x - 2592y - 52y

Combine like terms:

1803y = 1800x

Divide both sides by 1803:

y = x/1803

Next, substitute the value of y in the first equation:

x = 50x - 72(x/1803)

Simplify the equation:

x = 50x - 72x/1803

Combine like terms:

x = (90000x - 72x)/1803

Combine fractions:

x = 89728x/1803

Divide both sides by x:

1 = 89728/1803

Solve for x:

x = 89728/1803

Substitute the value of x back into the equation for y:

y = (89728/1803)/1803

Simplify:

y = 0.0496

Therefore, the solution to the linear system of differential equations is x = 89728/1803 and y = 0.0496.