Maths: differencial equations?

Find the general solution to the differential equation

d𝑢/d𝑣= 𝑎𝑢2

where 𝑎 is a constant.

4 Answers

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  • 3 weeks ago

    du/dv=au^2

    =>

    du/u^2=adv

    =>

    -1/u=av+C

    =>

    u=-1/(av+C)

    is the general solution.

  • 3 weeks ago

    Is that 2 an exponent? The convention for typing exponents without special software is to write du/dv = au^2.

    Assuming that's what you meant, I get

    du/u^2 = a dv =>

    1/u = -av + C =>

    u = 1/(C - av)

  • Ian H
    Lv 7
    3 weeks ago

    du/dv = au^2    ...   separable variables 

    ∫(1/u^2)du = a∫dv 

    -1/u + k = av 

    v = k/a – 1/au = C  – 1/au 

  • 3 weeks ago

    The answer is as follows:

    Attachment image
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