Differential Equations:

a) Find the general solution of differential equation y''+y'-6y=0

b) Find the solution of the same equation satisfying the initial condition y(0)=1, y'(0)= a. Then find a so that the solution approaches zero as t goes to + infinity.

Question

Differential Equations:

a) Find the general solution of differential equation y''+y'-6y=0

b) Find the solution of the same equation satisfying the initial condition y(0)=1, y'(0)= a. Then find a so that the solution approaches zero as t goes to + infinity.

amistre64 · Answer

constant coeffs are solved with an equivalent quadratic

amistre64 · Answer

r^2 +3 -6 = 0

y = c1 e^{r1x} + c2 e^{r2x}

lalaly · Answer

let y=e^(rx)
$$r^2+r-6=0$$$$(r+3)(r-2)=0$$$$r=-3,2$$$$y=c_1e^{-3x}+c_2e^{2x}$$

amistre64 · Answer

that 3 spose to be an r lol

amistre64 · Answer

part b is simply take the derivative of "y" and to solve for the boundary value stuff

amistre64 · Answer

i got no idea how that t to infinity part fits in tho

anonymous · Answer

that's cool. I'll try to figure that out. Thanks all!

amistre64 · Answer

good luck,

if I could see a"t" that could be limited that would help; but i think that is more material based to what you have and we lack.