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8 September, 04:06

Solve the given differential equation by finding, as in Example 4 from Section 2.4, an appropriate integrating factor. 4xy dx (4y 6x2) dy

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  1. 8 September, 06:37
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    y=1/6 · ln |x|+c.

    Step-by-step explanation:

    From Exercise we have the differential equation

    4xy dx = (4y6x²) dy.

    We calculate the given differential equation, we get

    4xy dx = (4y6x²) dy

    xy dx=6yx² dy

    6 dy=1/x dx

    ∫ 6 dy=∫ 1/x dx

    6y=ln |x|+c

    y=1/6 · ln |x|+c

    Therefore, we get that the solution of the given differential equation is

    y=1/6 · ln |x|+c.
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