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Math Help - Another First-Order Separable ODE

  1. #1
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    Another First-Order Separable ODE

    Find the solution of the differential equation that satisfies the given initial condition.

    (5+y^2)dy = y \cos(x) dx

    \frac{(5+y^2)}{y}dy = \cos(x) dx

    \int \frac{5}{y}dy + \int y dy = \int \cos(x) dx

    5 \ln|y| + \frac{1}{2}y^2 = \sin(x) + C

    The problem (this is on a web site) has the same left side of the equation that I have arrived at. It wants me to enter the right side of the equation. I tried entering \sin(\frac{\pi}{2}), but it rejected that solution.

    Does anybody see what they want me to enter here? Thanks.
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  2. #2
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    re: Another First-Order Separable ODE

    Looks o.k to me, do you need to solve for C maybe?

    Use x=0, y=1 gives C= 1/2
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  3. #3
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    re: Another First-Order Separable ODE

    That was it. Thanks. I couldn't see where they were going, but now I do.
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