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Math Help - [SOLVED] differential equation verification 2

  1. #1
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    [SOLVED] differential equation verification 2

    (1 + x^2) (dy/dx) = y with y(0) = 1 the answer i am getting is y = e^(arctan x) is this correct?? also for (dy/dt)(cos t) + y(sin t) = 1 with y(Pi/4) = sqrt(2) the answer i am getting is y = (cos t)(tan t) + (1/2)(sqrt(2)) is this correct?
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  2. #2
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    Yes, the first one is correct.

    The second should be y=Ccos(t)+sin(t)

    Using the initial condition, C=1.

    Therefore, y=cos(t)+sin(t)
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