Second Order Differential EquationDate: 11/04/2001 at 02:52:04 From: Roger Subject: 2nd order differential equations By letting p = dy/dx, solve y(d2y/dx2) = 2 (dy/dx)2 This is what I have done: d2y/dx2 = dp/dx y (dp/dx) = 2p2... ... ... Date: 11/04/2001 at 08:08:51 From: Doctor Anthony Subject: Re: 2nd order differential equations y.(d^2y/dx^2) = 2(dy/dx)^2 Since x is absent explicitly, put dy/dx = p and d^2y/dx^2 = p.(dp/dy) [We can prove this last expression from p = dy/dx dp/dy = d^2(y)/dx^2.(dx/dy) = (1/p).d^2(y)/dx^2 p.(dp/dy) = d^2(y)/dx^2 ] Our original equation can now be written y[p.dp/dy] = 2p^2 dp/p = 2dy/y ln(p) = 2.ln(y) + ln(A) ln(p) = ln[Ay^2] p = A.y^2 dy/dx = A.y^2 dy/y^2 = A.dx -1/y = A.x + B y = -1/(Ax+B) - Doctor Anthony, The Math Forum http://mathforum.org/dr.math/ |
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