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Math Help - calculus help!

  1. #1
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    calculus help!

    please help with these problems, any of them! it would be of great help! thanks!




    1. suppose that A is a constant. Verify that x(t)=1+t+Ae^t is a solution of the differential equation x'=x-t


    2. Suppose that A and B are constants. Verify that y(x)=A ln(x)+B+x is a solution of the differential equation xy''+y'=1
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by cottekr View Post
    please help with these problems, any of them! it would be of great help! thanks!




    1. suppose that A is a constant. Verify that x(t)=1+t+Ae^t is a solution of the differential equation x'=x-t


    2. Suppose that A and B are constants. Verify that y(x)=A ln(x)+B+x is a solution of the differential equation xy''+y'=1
    All you need to do is substitute the x(t) values given into the DE. I'll help you start the first one:

    since x(t)=1+t+Ae^t, we see that x'(t)=1+Ae^t

    Substituting this into the DE, we see that (1+Ae^t)=(1+t+Ae^t)-t

    I leave the simplification for you.

    This should give you enough help to do the second problem on your own.

    --Chris
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