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Thread: differential equation

  1. #1
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    differential equation

    some one please help me ive been trying to do this homework forever and i just dont know how. i have a few questions so as many that you could answer would be very helpful.

    verify the solution to the differential equation: y'' + y' + 2y=sinx, where y(x)=0.1sinx-0.3cosx.

    For the following questions you just need to gie a particular solution.

    y''' = sin(2x), y(0)=4, y'(0)=10, y''(0)= -8 ?

    square root of x * y' = 2(x^2)y - 5xy - 7y ?

    (10x^2 + 7x) / 2xy = y*y' ?

    (x^2)y^1 +(2x^3)y = 8x ?

    and lastly 2y'' +5y' - 6y = 0

    if someone could help me that be great thank you so much
    Last edited by CaptainBlack; Mar 22nd 2009 at 11:21 AM. Reason: it helps if the notation makes sense
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by coliechrist5 View Post
    verify the solution to the differential equation: y'' + y' + 2y=sinx, where y(x)=0.1sinx-0.3cosx.
    Differentiate $\displaystyle y(x)=0.1 \sin(x)-0.3 \cos(x)$ twice and then substitute $\displaystyle y$, $\displaystyle y'$ and $\displaystyle y''$ into the left hand side of the DE simplify and show that you are left with $\displaystyle \sin(x)$.


    CB
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