Y'' + 4y = ax + b how can i solve?

  • Thread starter c8c811
  • Start date
In summary, the conversation revolves around finding the solution for y(x) in the equation y'' + 4y = ax + b, where a and b are constants. The individual is seeking guidance on finding both the homogeneous and particular solutions, and is asking for either a rough guideline or detailed steps. They also ask for clarification on what form of solution to assume. The conversation ends with someone suggesting a particular solution of yp = Cx + D and asking for confirmation. The final comment questions if the conversation is about a homework problem.
  • #1
c8c811
2
0
y'' + 4y = ax + b

for y(x), and a & b are constants.

either rough guideline (for both homogeneous and particular solutions),
or detailed steps would be appreciated.

thanks in advance!
 
Physics news on Phys.org
  • #2
ok, i got the homogenous solution, but how do i get the particular one?

what form of solution can i assume??
 
  • #3
Try yp = Cx + D
 
  • #4
4y = ax + b is obviously going to satisfy it. will that do?:rolleyes:
 
  • #6
epenguin said:
4y = ax + b is obviously going to satisfy it. will that do?:rolleyes:
So what is y?
 
  • #7
Is it just me, or does this look like a homework problem?
 

FAQ: Y'' + 4y = ax + b how can i solve?

1. What is the meaning of the equation "Y'' + 4y = ax + b"?

The equation "Y'' + 4y = ax + b" is a second-order linear differential equation, where the second derivative of the dependent variable Y is added to four times the first derivative of Y. The right side of the equation contains the independent variables ax and b.

2. How is this equation solved?

To solve this equation, we need to use a method called "undetermined coefficients". This method involves finding a particular solution and a complementary solution, and then combining them to get the general solution.

3. What are the steps to solve this equation using undetermined coefficients?

The steps to solve this equation using undetermined coefficients are as follows:

  1. Find the complementary solution by setting the coefficients of the derivatives to zero.
  2. Find a particular solution by setting up a trial solution with undetermined coefficients and substituting it into the original equation.
  3. Find the values of the undetermined coefficients by equating the coefficients of the trial solution and the original equation.
  4. Combine the complementary solution and the particular solution to get the general solution.

4. Are there any other methods to solve this equation?

Yes, there are other methods to solve this equation, such as the method of variation of parameters and the Laplace transform method. However, the undetermined coefficients method is the most commonly used and easiest method for solving linear differential equations.

5. What are the applications of this type of equation in science?

This type of equation is commonly used to model physical systems in science, such as in mechanics, electromagnetism, and thermodynamics. It can also be used in economics, biology, and other fields to describe the behavior of systems that involve change over time.

Similar threads

I Where did this substitution technique go wrong?
Replies
27
Views
2K
I Explanation of all "its linearly independent derivatives"
Replies
3
Views
2K
I Find the general solution for the differential equation
Replies
4
Views
2K
I Solution of delayed forcing function
Replies
5
Views
2K
MHB B.2.2.16 IVP of \dfrac{x(x^2+1)}{4y^3}, y(0)=-\dfrac{1}{\sqrt{2}}
Replies
6
Views
1K
I Using complex numbers or phasor transform to solve O.D.E's
Replies
3
Views
2K
A How can I plot a 3D phase space for a system of differential equations?
Replies
4
Views
2K
Obtain a nonzero solution of ##y''-4y'+x^2(y'-4y)=0## by inspection
Replies
7
Views
1K
I Second order non-homogeneous linear ordinary differential equation
Replies
2
Views
2K
Assumptions about particular solutions
Replies
4
Views
2K

Hot Threads

Recent Insights

Back
Top