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anonymous
 one year ago
Differential Equations SOS PLEASE
anonymous
 one year ago
Differential Equations SOS PLEASE

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[y'''+y'=\frac{ sinx }{ \cos^2x }\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0meaning \[K1=0, K2,3= +i\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[Y=C1+C2\cos(x)+C3\sin(x)+Yp\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0now how do I find Yp?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0should I find the derivative ?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3familiar with variation of parameters ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I really need help with this one

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3\[y'''+y'=\frac{ \sin x }{ \cos^2x }\] Let \( y'=v\), then the DE becomes \[v''+v=\frac{ \sin x }{ \cos^2x }\] which is a familiar second order ordinary eqn, you can find \(Y_p\) using wrokskian or any other tricks that you're familiar with

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0hmmmm not sure I'm following

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I found the general solution

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0All I need now is the private one

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Are you familiar with the method I'm using?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3\[v''+v=\frac{ \sin x }{ \cos^2x }\] earlier you worked the general solution, general solution for above reduced DE is \(c_2\cos x+c_3\sin x\), yes ?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3No, we're only looking at reduced DE for now.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Can you please show how to do it using the formula you've attached?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3Okay, so from general solution we have \(y_1 = \cos x\) \(y_2 = \sin x\) Wronkskian\(W(y_1, y_2) = \begin{vmatrix} \cos x &\sin x\\\cos'x&\sin'x\end{vmatrix} = \cos^2x+\sin^2x = 1 \)

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3simply plug it in the formula and evaluate the integral(s)

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3g(t) is whatever there on the right hand side

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3\(g(\color{red}{x}) = \dfrac{\sin x}{\cos^2x}\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0and how do I find C1 then?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3we will worry about that in the very end

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3Keep in mind we're solving the "reduced" DE in \(v\)'s completely first, then we're gona substitute back \(v\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I think I can handle with that by myself, but how then can I find C1?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3\(\large v(x) = c_2\cos x + c_3\sin x+Y_p\) plug in \(v(x) = y'\) back

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0thank you so much @ganeshie8 !

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I think I've got it! I'll try at home and see if it works out for me

ikram002p
 one year ago
Best ResponseYou've already chosen the best response.1good question, it was useful for me as well .

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3you may refer to this solution generated by wolfram if you get stuck..

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.1Y_h portion is always easier than finding the Y_p

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.1there are 3 different ways to solve 2nd order odes... method of undetermined coefficients, variation of parameters, and laplace transform. It's just that sometimes one method is easier to use than the other 2. >_<
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