MHB What are the solutions and domains for Homogenous Linear Equations (Wave)?

ineedhelpnow
Messages
649
Reaction score
0
(Wave)
i have a test on friday that I am studying for so i was working through some problems in my textbook. i came across this question and I am stuck on what to do. can anyone help me out?
thanks
View attachment 4128
 

Attachments

  • 321.png
    321.png
    4.6 KB · Views: 104
Physics news on Phys.org
What you can do here is take the first and second derivatives (with respect to $x$) of the solutions given and substitute them into the given ODE and see if an identity results. For example, let's do $y_1$:

$$y_1=e^{2x}$$

And so we find:

$$y_1'=2e^{2x}$$

$$y_1''=4e^{2x}$$

And then substituting these into the ODE, we find:

$$4e^{2x}-7\cdot2e^{2x}+10e^{2x}=0$$

$$0=0$$

Thus, we know $y_1$ is a solution of (A). Try the other two...:D
 
I understand now ^^ but what if it were on a different interval from like 0 to 1 instead. Would that make a difference or does it mean that the function only exists on this interval?
 
As given, the solutions are defined for all real $x$. The ODE and/or solution will tell you where the solution is defined, either explicitly, or implied. :D
 
Back
Top