Solving System of Coupled DEs: Parametrized Curve Solution

[Si-duck]

Consider a system of coupled differential equations

x'=5x-y where x(0) = 6
y'=-x+5y where y(0)=-4

a) Show that the parametrised curve (x,y)= r(t)=(exp(4t) + 5exp(6t), exp(4t) - 5exp(6t))

How would you go about showing this?

 

[jackmell]

Consider a system of coupled differential equations

x'=5x-y where x(0) = 6
y'=-x+5y where y(0)=-4

a) Show that the parametrised curve (x,y)= r(t)=(exp(4t) + 5exp(6t), exp(4t) - 5exp(6t))

How would you go about showing this?

You just substitute them into the DEs. Keep in mind that x' is really dx/dt and y' is dy/dt. Ok then, differentiate the solutions, put them on the left sides, then substitute the solutions for x(t) and y(t) on the right and see if they're equal.