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anonymous
 one year ago
Find the two values of k for which y(x) = e^(kx) is a solution of the differential equation y"  4y' + 0y = 0
anonymous
 one year ago
Find the two values of k for which y(x) = e^(kx) is a solution of the differential equation y"  4y' + 0y = 0

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ChillOut
 one year ago
Best ResponseYou've already chosen the best response.1All right, first we should have \(k²*e^{kx}4ke^{kx}=0\)

ChillOut
 one year ago
Best ResponseYou've already chosen the best response.1which leads to \((k4)*k*e^{kx}=0\)

ChillOut
 one year ago
Best ResponseYou've already chosen the best response.1Now you are able to finish it.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Woah woah woah, diff eq's aren't my strong suit, I'm just getting started. could you walk me into getting the k^2 * e^(kz)4ke^(kx) = 0?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Is it just doing second derivative of the function, and the first derivative, then subbing into the form given?

ChillOut
 one year ago
Best ResponseYou've already chosen the best response.1All right. For differential equations you must know derivatives... The differential equation in question \((y''(x)4y'(x)+0y=0\)) is a second order linear ordinary differential equation, y''(x) is the second derivative of y(x) and y'(x) is the first derivative.

ChillOut
 one year ago
Best ResponseYou've already chosen the best response.1All I did was the differentiation of the given solution. Afterwards I plugged the solution in the equation.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So with this all plugged in now, I want to solve for x = 0? Or find k in terms of x?

ChillOut
 one year ago
Best ResponseYou've already chosen the best response.1No, you don't want to solve in terms of x. You want find a value for k in which the lefthand side is equal to the righthand side. (This is stated in the beggining of the question).

ChillOut
 one year ago
Best ResponseYou've already chosen the best response.1The question doesn't asks for values x, and most likely will never ask, unless it is a boundary value problem or initial value problem.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So I just want values for k that will make \[ke ^{kx}(k4)\] equal to zero? I'm sorry if I'm still a little confused

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Wow, that was easier than I expected

ChillOut
 one year ago
Best ResponseYou've already chosen the best response.1When it gives you a solution, you will want to plug that solution and its derivatives in the ODE. That's how this kind of question is done.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ODE being Order of Diff Eq's? Will the form given in this problem always be the same?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Meaning y"  4y' + 0y = 0

ChillOut
 one year ago
Best ResponseYou've already chosen the best response.1Nope, Ordinary Differential Equation. We have the PDEs too, but that's later for you :P

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Can I ask one more question on this topic? I've done out the work but can't see where Differential Equations fit in

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0The solution of a certain differential equation is of the form \[y(t)=ae ^{2t} + be ^{3t}\] where a and b are constants. The solution has initial conditions y(0) = 4 and y'(0) = 3. Find the solution bu using the initial conditions to get linear equations for a and b

ChillOut
 one year ago
Best ResponseYou've already chosen the best response.1Show me what you have done until now.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I did it out, and I'm pretty sure that a = 1 and b = 5. I thought I was supposed to thenn just substitute those numbers in for a and b, and call it a day, but my homework program says that's wrong

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0f(0)=4, so a+b should =4, and we can get a = 4b

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Then I found the derivative, y'(t) = 2ae^(2t)+3be^(3t)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Subbed in 0 and set it equal to 3, where I found that 3 = 8b, so b = 5

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Then I went back and subbed the new b into a = 4b to get a = 1

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Submitted as an answer 1e^(2t)+5e^(3t) but webwork said it was wrong

ChillOut
 one year ago
Best ResponseYou've already chosen the best response.1Well, I dunno how they accept the answers, so in this one I can't help you :(

ChillOut
 one year ago
Best ResponseYou've already chosen the best response.1But yes, you did it right.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Huh... Okay, well thanks again man!
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