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second order differential equations watch

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    :confused: Can someone show me how to do the following please.

    1.) dy/dx = y(x+2y) / x(y+2x), y=vx

    2.) (x+y)dy/dx = x^2 + xy + x + 1, y=v-x

    3.) x^2(d^2y/dx^2) + x(dy/dx) + y = 0, x=e^v
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    1) dy/dx = y(x+2y) / x(y+2x), y=vx

    y = vx
    dy/dx = x(dv/dx) + v

    y(x+2y) / x(y+2x)
    = vx(x+2vx)/ x(vx+2x)
    = v(1+2v)/(v+2)

    -> x(dv/dx) + v = v(1+2v)/(v+2)
    -> x(dv/dx) = (v^2 - v)/(v+2)
    -> (v+2)/(v^2 - v) dv = dx/x

    I guess you can do it from now.
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    The others just do it simliarly, I think you'll get the answer.

    After you get v = f(x), then subsitute into y = vx to get y = g(x)
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    K thanks BCHL85, i'll give them a go.
 
 
 
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