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Your selection of yp is confusing. It is recommended that if the RHS is a polynomial of order n, then yp = a general polynomial of order n, not order n+1.werson tan said:Homework Statement
i gt stucked here ... how to continue ? what's wrong with my working ? i found 2 values for D , whcih is wrong
Homework Equations
The Attempt at a Solution
then , what is the correct yp ?SteamKing said:Your selection of yp is confusing. It is recommended that if the RHS is a polynomial of order n, then yp = a general polynomial of order n, not order n+1.
See:
http://tutorial.math.lamar.edu/Classes/DE/UndeterminedCoefficients.aspx
A and E are solitary constants. You don't need to multiply your initial choice of yp by x.werson tan said:then , what is the correct yp ?
i choose my initial yp = cX^2 + Dx + E , nut i found that the term E is similar to the A , so i multiply the initial yp with x , to get my new yp
i have redo the question , i got Acos2x + Bsin2x +0.25x^2 + 3/2 , but the ans given is Acos2x + Bsin2x +0.25x^2 +3/8HallsofIvy said:Your difficulty is that your solution to the associated homogeneous equation is wrong! The associated homogeneous equation is y''+ 4y= 0 which has characteristic equation [itex]m^2+ 4= 0[/itex] with solutions 2i and -2i. You have written the characteristic equation as [itex]m^2+ 4m= 0[/itex] which has solutions m= -4 and m= 0. That would correspond to differential equation y''+ 4y'= 0.
Check your arithmetic or provide your work to obtain this solution.werson tan said:i have redo the question , i got Acos2x + Bsin2x +0.25x^2 + 3/2 , but the ans given is Acos2x + Bsin2x +0.25x^2 +3/8
i have attached the working in the picture uploaded aboveSteamKing said:Check your arithmetic or provide your work to obtain this solution.
I deleted the picture you attached. It was extremely hard to read, with the top so dark it was nearly impossible to read, and portions were cut off.werson tan said:i have redo the question , i got Acos2x + Bsin2x +0.25x^2 + 3/2 , but the ans given is Acos2x + Bsin2x +0.25x^2 +3/8
It's gone now. We would prefer that you show your work here in the input pane, rather than in a poor quality image with bad lighting and information cut off.werson tan said:i have attached the working in the picture uploaded above
"Stucked" is not a word in English. You can get stuck or you got stuck, but you can't get "stucked."werson tan said:i gt stucked here
Mark44 said:"Stucked" is not a word in English. You can get stuck or you got stuck, but you can't get "stucked."
The concept of "Undetermined coefficient" refers to a method used in solving differential equations. It involves assuming a general form of the solution and then finding the coefficients that satisfy the equation.
In the Undetermined coefficient method, we first assume a general form of the solution, which in this case is y = Ax^2 + Bx + C. Then, we substitute this into the original equation and solve for the coefficients A, B, and C by comparing the coefficients of the same powers of x on both sides of the equation.
No, there are other methods such as the variation of parameters and the Laplace transform method. The choice of method depends on the type of differential equation and the available initial conditions.
The Undetermined coefficient method is relatively simple and straightforward to use. It also gives a general solution that can be easily adapted to different initial conditions.
Yes, the Undetermined coefficient method can only be applied to linear differential equations with constant coefficients. It also may not work for all types of functions on the right-hand side of the equation, such as trigonometric functions or exponential functions.