Advanced Engineering Mathematics, 7th Edition

3.7 Nonlinear Equations

INTRODUCTION

The difficulties that surround higher-order nonlinear DEs and the few methods that yield analytic solutions are examined next.

Some Differences

There are several significant differences between linear and nonlinear differential equations. We saw in Section 3.1 that homogeneous linear equations of order two or higher have the property that a linear combination of solutions is also a solution (Theorem 3.1.2). Nonlinear equations do not possess this property of superposability. For example, on the interval (−∞, ∞), y₁ = e^x, y₂ = e^−x, y₃ = cos x, and y₄ = sin x are four linearly independent solutions of the ...