# Thread: For what values of r does the function y = e^rx satisfy

1. ## For what values of r does the function y = e^rx satisfy

For what values of r does the function y = e^rx satisfy the equation y'' + 4y' - 45y = 0?

2. Solve $r^2+4r-45=0$ do you know why?

3. Hello,

Why don't you just try to plug y = e^rx into the given equation and see what happens? You should notice that e^rx is never equal to zero, so this will lead you to a polinomial equation in r. Solve it and find the roots - they are what you're looking for.

4. Originally Posted by pickslides
Solve $r^2+4r-45=0$ do you know why?
i do not know why. please explain

5. An eqn in the form $y''+ay'+by=0$ has a characteristic eqn $r^2+ar+b=0$ which gives the solution to the original D.E for real values of $r$ in the form $y = e^{rx}$

Did you solve for $r$ ? What did you get?

6. 9, -5
what is D.E. ?

7. Better double check your workings, $r = -9, 5$ , D.E = differential equation.

8. Originally Posted by pickslides
Better double check your workings, $r = -9, 5$ , D.E = differential equation.
heehee my mistake thank you!