need math wiz to confirm if my equation is right and help find values for symbol

[RayEarth]

problem: find the values of "h" for which y=e^hx satisfies the equation y+y'=y"

note: "h" is a symbol that looks like an upside down "y" in the textbook, not sure if this makes a difference.

i got the following so far:
y=e^hx
y'=h*e^hx
y"=h^2*e^hx

then i just plugged in the values into the equation to get: e^hx+h*e^hx=h^2*e^hx
now if my equation is right so far, how would i go about finding the values of "h" that satisfies this equation i found?

this is an even problem so i can't verify if the answers are correct.

 

[Orsorum]

h is lambda. No, it doesn't make that much of a difference. 😛

 

[silverpig]

Originally posted by: RayEarth
problem: find the values of "h" for which y=e^hx satisfies the equation y+y'=y"

note: "h" is a symbol that looks like an upside down "y" in the textbook, not sure if this makes a difference.

i got the following so far:
y=e^hx
y'=h*e^hx
y"=h^2*e^hx

then i just plugged in the values into the equation to get: e^hx+h*e^hx=h^2*e^hx
now if my equation is right so far, how would i go about finding the values of "h" that satisfies this equation i found?

this is an even problem so i can't verify if the answers are correct.

Dude, you did all the hard stuff. Just plug all that into your second equation.

y+y'=y"

substitute in what you found

e^hx + h*e^hx = h^2*e^hx

divide all by e^hx

1 + h = h^2

I'm sure you can take it from here 🙂

 

[RayEarth]

thanks for quick replys, i'll try to finish what i have as soon as i can

 

[DrPizza]

<-- agrees with silverpig..... just solve the remaining quadratic equation.

 

[RayEarth]

it seems like an odd final answer but i got: 1 +or- square root of 5 divided by 2 for all values "h" can be, anyone get the same thing? i used the quad formula on the equation h^2-h-1=0 after dividing everything out.