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    Find the general solution to the differential equation
     \displaystyle \frac{d^2y}{dx^2}-3\frac{dy}{dx}+2y=\sin^2 x .
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    (Original post by Ano123)
    Find the general solution to the differential equation
     \displaystyle \frac{d^2y}{dx^2}-3\frac{dy}{dx}+2y=\sin^2 x .
    My first thought is to try y=Asin^2(x)+Bcos^2(x)+Csin(x)cos (x)+De^x + Ee^2x

    There are proper methods for finding the general one :s (and I can't exactly recall them)

    You could do the CF method on top of that I guess?
    (Setting it = 0, finding the auxiliary equation and then adding multiples of the answer that gives you (which would be De^x+Ee^2x) to a single found solution (which would be the Asin^2x etc))

    I love not being coherent
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    (Original post by Ano123)
    Find the general solution to the differential equation
     \displaystyle \frac{d^2y}{dx^2}-3\frac{dy}{dx}+2y=\sin^2 x .
    Do you usually just post the question for others to answer without giving any shown attempt or...?

    \displaystyle \sin^2x=\frac{1}{2}[1-\cos(2x)] for simplicity.
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    (Original post by Ano123)
    Find the general solution to the differential equation
     \displaystyle \frac{d^2y}{dx^2}-3\frac{dy}{dx}+2y=\sin^2 x .
    What have you tried so far?
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    (Original post by Ano123)
    Find the general solution to the differential equation
     \displaystyle \frac{d^2y}{dx^2}-3\frac{dy}{dx}+2y=\sin^2 x .
    Disappointed in you. Normally I look at your questions and say wtf is going on. This one I can actually do!
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    (Original post by IYGB)
    Disappointed in you. Normally I look at your questions and say wtf is going on. This one I can actually do!
    Yeah he's been slacking lately. That square in a circle was pretty straight forward and now this!

    Someone's losing their game, it seems.
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    (Original post by Ano123)
    Find the general solution to the differential equation
     \displaystyle \frac{d^2y}{dx^2}-3\frac{dy}{dx}+2y=\sin^2 x .
    Are you going to post some of your thoughts on this, or do you just want everyone else to do the work for you?
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    (Original post by IYGB)
    Disappointed in you. Normally I look at your questions and say wtf is going on. This one I can actually do!
    I thought the particular integral was tough but the double angle formula makes it easy. I used variation of parameters and now feel a bit silly it was so easy.
 
 
 
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