The Single First Order Equation

Part of the Applied Mathematical Sciences book series (AMS, volume 1)


The first order equations, in general, present interesting geometric interpretations. It will be convenient then to restrict the discussion to the case of two independent variables, but it will be made clear that the theory can be extended immediately to any number of variables. We consider then equations of the form
$$ F(x,y,u,{u_x},{u_y}) = F(x,y,u,p,q) = 0 $$
where we have used the notation ux = p, uy = q. A solution z = u(x, y), when interpreted as a surface in three dimensional space, will be called an integral surface of the differential equation.


Characteristic Equation Characteristic Curve Order Equation Parameter Family Tangent Plane 
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Copyright information

© Springer-Verlag New York Inc. 1975

Authors and Affiliations

  • F. John
    • 1
  1. 1.Courant InstituteNew York UniversityNew YorkUSA

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