For what values of r does the function e^(rx) satisfy the equation y''+5y' -6y=0 (Note: r is a constant.) For what values of r does the function e^(rx) satisfy the equation y''+5y' -6y=0 (Note: r is a constant.) @Mathematics

Question

For what values of r does the function e^(rx)  satisfy the equation y''+5y' -6y=0  (Note: r is a constant.) For what values of r does the function e^(rx)  satisfy the equation y''+5y' -6y=0  (Note: r is a constant.) @Mathematics

myininaya · Answer

solve $$r^2+5r-6=0$$

myininaya · Answer

$$(r+6)(r-1)=0$$

myininaya · Answer

r=-6
r=1

anonymous · Answer

did you just take the derivative of e^rx with respect to r and the second derivative and then plug it in the equation?

myininaya · Answer

$$y=e^{-6x}+e^{1x}$$ <- you can check this if you want

myininaya · Answer

$$ay''+by'+cy=0$$
all you have to do to find value of r is solve
$$ar^2+br+c=0$$

anonymous · Answer

okay i see thank you

myininaya · Answer

oh and to give a more general answer we say
$$y=c_1 e^{-6x}+c_2e^{x}$$
c_1,c_2 are constants