Ordinary Differential Equations |
Contents
INTRODUCTION | 3 |
FIRSTORDER DIFFERENTIAL | 17 |
LINEAR DIFFERENTIAL EQUATIONS | 31 |
Copyright | |
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arbitrary Ax² boundary-value problem bounded C₁ C₁ and C₂ C₁x C₂ C₂)ex Chapter characteristic polynomial constant coefficients continuous function derivative differentiable function differential equation y(n dy/dx end points ential equation equa equation L(y erix Euler's formula Examples Exercise existence theorem f satisfies family of curves ferential equation find a solution Find the solution first-order differential equation first-order equation function y(x g(yo given point xo given values global Lipschitz condition H₁ Hence homogeneous equation inhomogeneous initial values initial-value problem instance integral linear differential equation lution mean value theorem order differential equation original equation P₁ Partial Differential Equations Peano existence theorem polygon proof r₁ real-valued function satisfies a global set of solutions solu solution curve Solve the differential tangent trigonometric function unique solution uniquely determined whole plane x²y y₁ хо