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

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In summary, the conversation is about finding the particular solution for the given ODE, which involves using the characteristic equation to find the complementary solution and then using the guessing method to find the particular solution. The conversation also discusses mistyping the function and the ease of solving the problem with a different function.
  • #1
final_d3stinati
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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!
 
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  • #2
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 :confused:
 
  • #3
final_d3stinati said:
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)
:devil:
 
  • #4
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!
 
  • #5
no!
sqrt(3^2-4(-10))=sqrt(49)=7
 
  • #6
final_d3stinati said:
no!
sqrt(3^2-4(-10))=sqrt(49)=7

:eek:

true true :biggrin:


see what happens when you are a year out of college you forget basic stuff :frown:
 
  • #7
Oops!
It was very easy! I got it.
Guessing Method:
Yp= k*exp(x) ---> Yp=-exp(x)/12
 

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

What is an ODE?

An ODE, or ordinary differential equation, is a mathematical equation that relates a function to its derivatives. It is commonly used in physics and engineering to model systems that change over time.

What is Yp in relation to an ODE?

Yp, or particular solution, is a specific solution to an ODE that satisfies both the original equation and any initial or boundary conditions. It is used to find the general solution to the ODE.

How do you find Yp for an ODE?

To find Yp, you can use different methods such as variation of parameters, undetermined coefficients, or the method of annihilators. These methods involve solving for coefficients or parameters that satisfy the given ODE.

Why is Yp important in solving an ODE?

Yp is important because it allows us to find the general solution to an ODE. This general solution includes both the particular solution and the complementary solution, which represents the family of all possible solutions.

Can Yp be used to solve any ODE?

No, Yp can only be used to solve linear ODEs with constant coefficients. Nonlinear ODEs may require different methods for finding particular solutions.

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