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Math Help - general solution of ode

  1. #1
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    general solution of ode

    Question: find the general solution of xX' = aX
    iknow it's kinda simple ode.. but, i just dont know y i cant get the correct answer..

    solution..

    xX' = aX
    x dX/dx = aX
    d/dx X = aX/x
    X = ∫aX/x dx
    X = aX ln |x| + C

    the general solution is Ax^a

    problem : i cant get the correct answer..
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  2. #2
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    Quote Originally Posted by nameck View Post
    Question: find the general solution of xX' = aX
    iknow it's kinda simple ode.. but, i just dont know y i cant get the correct answer..

    solution..

    xX' = aX
    x dX/dx = aX
    d/dx X = aX/x
    X = ∫aX/x dx
    X = aX ln |x| + C

    the general solution is Ax^a

    problem : i cant get the correct answer..
    I'll use x's and y's - it's a little easier.

     <br />
x \frac{dy}{dx} = ay \; \text{(we separate)}\; \frac{dy}{y} = a \frac{dx}{x}<br />

    integrating gives

     <br />
\ln y = a \ln x + c \; \text{(let} c = \ln A)<br />

    so

     <br />
\ln y = \ln A + a\ln x = \ln Ax^a<br />
    giving


     <br />
y = Ax^a.<br />
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  3. #3
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    I'll use x's and y's - it's a little easier.

    can i simply change the variable?
    bcoz, X is equal tu X(x) function of x..
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  4. #4
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    Quote Originally Posted by nameck View Post
    I'll use x's and y's - it's a little easier.

    can i simply change the variable?
    bcoz, X is equal tu X(x) function of x..
    Sure. Just keep it straight and remember to switch back in the end.
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