MHB Solving an ODE: Seeking c so y'(0)=0

  • Thread starter Thread starter mariask
  • Start date Start date
  • Tags Tags
    Ode
mariask
Messages
1
Reaction score
0
so I am trying to solve this equation y'+5.6y=9.5cos(2x)+2.4sin(2x) . I want the c in order to y'(0)=0. I am really lost
 
Physics news on Phys.org
Do you know how to do the method of undetermined coefficients? Please let us know what you've done.

-Dan
 
mariask said:
so I am trying to solve this equation y'+5.6y=9.5cos(2x)+2.4sin(2x) . I want the c in order to y'(0)=0. I am really lost
There is NO "c" in what you wrote! Do you mean the constant in the solution? It isn't necessarily called "c"!

The general solution to the associated homogenous equation, y'+5.6y= 0, is [math]y= Ce^{-5.6x}[/math]. To find a solution to the entire equation, let [math]y= Acos(2x)+ Bsin(2x)[/math]. Then [math]y'= -2Asin(2x)+ 2Bcos(2X)[/math] and the [math]y'+ 5.6y= -2Asin(2x)+ 2Bcos(2x)+ 5.6Acos(2x)+5.6Bsin(2x)= (-2A+ 5.6B)sin(2x)+ (2B+ 5.6A)cos(2x)= 2.4sin(2x)+ 9.5cos(2x)[/math].

Since this to be true for all x, we must hav -2A+ 5.6B= 2.4 and 2B+ 5.6A= 9.5.

Solve those two equations for A and B. Then the solution to the entire equation is [math]y= Ce^{-5.6x}+ Acos(2x)+ Bsin(2x)[/math] for those A and B. Then [math]y'= -0.56Ce^{-5.6x}- 2Asin(2x)+ 2Bcos(2x)[/math] so that [math]y'(0)= -0.56C+ 2B= 0[/math]. [math]C= (2/0.56)B[/math] where B was found before.
 
Last edited:

Thread 'Volterra equation of the second kind'

There is the following linear Volterra equation of the second kind $$ y(x)+\int_{0}^{x} K(x-s) y(s)\,{\rm d}s = 1 $$ with kernel $$ K(x-s) = 1 - 4 \sum_{n=1}^{\infty} \dfrac{1}{\lambda_n^2} e^{-\beta \lambda_n^2 (x-s)} $$ where $y(0)=1$, $\beta>0$ and $\lambda_n$ is the $n$-th positive root of the equation $J_0(x)=0$ (here $n$ is a natural number that numbers these positive roots in the order of increasing their values), $J_0(x)$ is the Bessel function of the first kind of zero order. I...
View full post »

Thread 'Visual Representation of Separation of Varables'

Are there any good visualization tutorials, written or video, that show graphically how separation of variables works? I particularly have the time-independent Schrodinger Equation in mind. There are hundreds of demonstrations out there which essentially distill to copies of one another. However I am trying to visualize in my mind how this process looks graphically - for example plotting t on one axis and x on the other for f(x,t). I have seen other good visual representations of...
View full post »

Similar threads

A Seeking advice about solving an ODE
Replies
3
Views
3K
I When is an ODE (numerically) reversible in time?
Replies
4
Views
2K
I Question about solving linear first order non-homogeneous ODEs
Replies
3
Views
3K
I Converting Second Order ODE to Hypergeometric Function
Replies
7
Views
3K
A Help with understanding why limit implies uniqueness
Replies
1
Views
2K
MHB Solving a Non-Exact ODE: $(y-2x^2y)dx +xdy = 0$
Replies
4
Views
2K
MHB -b.2.2.26 IVP min value y'=2(1+x)(1+y^2); y(0)=0
Replies
3
Views
1K
I Can the ODE \psi''-y^2\psi=0 be solved using a general method?
Replies
2
Views
3K
I Understanding Euler Method: Finding Initial Condition of y(0)=1
Replies
7
Views
4K
POTW Solve Linear System of ODEs: x',y' w/ Initial Conditions x(0),y(0)
Replies
10
Views
2K

Hot Threads

Recent Insights

Back
Top