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Can someone check a couple of these?

  1. Feb 13, 2006 #1
    Are these the correct answers for the following questions?

    1 Solve the Bernoulli equation.

    a) [tex]x\frac{dy}{dx}+67=3xy^\frac{4}{3}[/tex]

    What I got:
    [tex]\frac{1}{y^\frac{1}{3}}=x+cx^2[/tex]


    b) [tex]x^2y'+2xy=5y^4[/tex]

    What I got:
    [tex]2y^(-3)=\frac{30}{13}\frac{1}{x}+cx^12[/tex]


    2 Solve each differential equation.

    a) [tex]xy''+2y'=6x[/tex]

    What I got:
    I let u=y', y''=du/dx
    [tex]y=x^2-\frac{c_1}{x}+c_2[/tex]

    b) [tex]y^3y''=1[/tex]

    What I got:
    I let u=y', y''=udu/dy
    [tex]y=c_1\sqrt{csc(x+c_2)}[/tex]
     
    Last edited: Feb 13, 2006
  2. jcsd
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