Question

Solve the system of differential equations:{ x' =250x−196y/y′=315x−247y Subject to the initial conditions: x(0)=8, y(0)=10 Please proceed with solving this system of differential equations and provide the solution without the final answer.

Answer 1

To solve the system of differential equations, use the method of elimination to eliminate x and y, then solve for x and substitute the value into one of the original equations to find y.

Step-by-step explanation:

To solve the system of differential equations:

x' = 250x - 196y

y' = 315x - 247y

we can use the method of elimination. Here are the steps:

1. Multiply the first equation by 315 and the second equation by 250 to eliminate x.
2. Subtract the two equations to eliminate y.
3. Solve the resulting equation for x.
4. Substitute the value of x into one of the original equations to solve for y.

Using the initial conditions x(0) = 8 and y(0) = 10, we can find the final solution.