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单词 homogeneous first‐order differential equation
释义
homogeneous first‐order differential equation

Mathematics
  • A first‐order differential equation dy/dx = f(x,y) in which the function f, of two variables, has the property that f(kx,ky) = f(x,y) for all k. Examples of such functions are

    x2+3y22x25xy,1+ex/y,xx2+y2.

    Any such function f can be written as a function of one variable v, where v = y/x. The method of solving homogeneous first‐order differential equations is to let y = vx so that dy/dx = x(dv/dx) + v. The differential equation for v as a function of x that is obtained is always separable.


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