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Math Help - Differential equation- unfamiliar forms

  1. #1
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    Differential equation- unfamiliar forms

    a. 4+xdy/dx=y^2
    b. e^ydy/dx-1=inx
    c.ycosxdy/dx=2-ydy/dx

    It would be fine if you just do one- but if anyone is feeling bored-
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  2. #2
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    Hello, kingkaisai2!

    These are all separable . . .


    a)\;\; 4 + x\frac{dy}{dx}\:=\:y^2

    We have: . x\frac{dy}{dx}\:=\:y^2 - 4\quad\Rightarrow\quad \frac{dy}{y^2 - 4} \:=\:\frac{dx}{x}



    b)\;\; e^y\frac{dy}{dx} - 1 \:=\:\ln x

    We have: . 1 + \ln x)\,dx" alt="e^y\frac{dy}{dx} \:=\:1 + \ln x\quad\Rightarrow\quad e^y\,dy \:=\1 + \ln x)\,dx" />



    c)\;\;y\cos x\frac{dy}{dx} \:=\:2 - y\frac{dy}{dx}{

    We have: . y\cos x\frac{dy}{dx} + y\frac{dy}{dx}\:=\:2

    Factor: . y\frac{dy}{dx}(\cos x + 1) \:=\:2\quad\Rightarrow\quad y\,dy \:=\:\frac{2\,dx}{\cos x + 1}


    And the rest is "only Calculus" . . . LOL!

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