Question

can you help me solve x' = 5x + 7y, y' = 2x + 10y for x(t) and y(t) using the method of elimination? I have the initial conditions x(0) = 1 and y(0) = 5, but I cannot find my coeff. A and B correctly.

Answer 1

From the second equation
2x = y' - 10y

hence
x = (1/2)(y' - 10y)
and
x' = (1/2)(y'' - 10y)

Now substitute that into the first equation and you will have a second order equation in y.

Solve, then find x using one of the equations above.