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Math Help - Find particular solution by substitution

  1. #1
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    Find particular solution by substitution

    1.By substitution y = vx , show that x(x+y)dy/dx = x^2 + y^2 is y + x ln ((x-y)^2 /x) = 0 when y = 0 and x = 1.
    2.dx/dt = g(1- e^-kt)/k , express x in terms of g,k and t.
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    Re: Find particular solution by substitution

    Okay, if y= vx, then dy/dx= v+ x dv/dx. What do you get when you replace y by vx and dy/dx by v+ x dv/dx?

    The second looks like a straightforward integration.
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    Re: Find particular solution by substitution

    Are g and k constants?
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    Re: Find particular solution by substitution

    Quote Originally Posted by Prove It View Post
    Are g and k constants?
    Yes

    Quote Originally Posted by HallsofIvy View Post
    Okay, if y= vx, then dy/dx= v+ x dv/dx. What do you get when you replace y by vx and dy/dx by v+ x dv/dx?

    The second looks like a straightforward integration.
    I got dv/dx = (x+v-vx-xv^2)/(x^2 + vx^2), what's next? How can I solve this?
    The second is exactly the straightforward integration, but I'm not able to solve it.......Some guide, please?
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