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20 September, 09:26

In this problem, y = 1 / (x2 +

c. is a one-parameter family of solutions of the first-order de y' + 2xy2 = 0. find a solution of the first-order ivp consisting of this differential equation and the given initial condition. y (4) = 1/15

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  1. 20 September, 10:49
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    A family of solutions to the DE is given to be y = 1 / (x^2 + c);

    With given initial condition y (4) = 1/15.

    Let's use this initial data to find a particular solution.

    Plug 4 in for x, and 1/15 in for y,

    1/15 = 1 / (4^2 + c)

    Solve for c.

    Reciprocate each side,

    15 = 4^2 + c

    -1 = c

    Plugging this c value back into our family of solutions will give us one particular solution to the DE,

    y = 1 / (x^2 - 1)
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