How Do You Solve Yp for the ODE y'' - 3y' - 10y = exp(x)?

[final_d3stinati]

Edit: SOLVED!
**********************
Please help me find Yparticular for this ODE:

y''-3y'-10y=exp(x)
...
m^2-3*m-10=0 -> Yh = c1*exp(-5x)+c2*exp(2x)
Yp = ?

Thank you!

 

[final_d3stinati]

This was a question in my midterm exam which I coudn't figure out. My midterm is over now! I just want to find the answer

 

[cronxeh]

Please help me find Yparticular for this ODE:

y''-3y'-10y=exp(x)
...
m^2-3*m-10=0 -> Yh = c1*exp(-5x)+c2*exp(2x)
Yp = ?

Thank you!

Aww you changed it to exp(x)

 

[final_d3stinati]

sorry! I mistyped.. in case of exp(1), it was very easy! Yh=-exp(1)/10
exp(x) makes it really hard for me! I can't use Guessing mehtod or even Wronskian!

 

[final_d3stinati]

no!
sqrt(3^2-4(-10))=sqrt(49)=7

 

[cronxeh]

no!
sqrt(3^2-4(-10))=sqrt(49)=7

true true


see what happens when you are a year out of college you forget basic stuff

 

[final_d3stinati]

Oops!
It was very easy! I got it.
Guessing Method:
Yp= k*exp(x) ---> Yp=-exp(x)/12