A nonlinear differential equation is generally more difficult to solve than linear equations. On the other hand, nonlinear differential equations involve nonlinear terms in any of y, y′, y″, or higher order term. with f( x) = 0) plus the particular solution of the non-homogeneous ODE or PDE. The general solution of non-homogeneous ordinary differential equation (ODE) or partial differential equation (PDE) equals to the sum of the fundamental solution of the corresponding homogenous equation (i.e. ( 1), if f( x) is 0, then we term this equation as homogeneous. A differential equation is termed as linear if it exclusively involves linear terms (that is, terms to the power 1) of y, y′, y″ or higher order, and all the coefficients depend on only one variable x as shown in Eq. The differential equation can also be classified as linear or nonlinear. To begin with, a differential equation can be classified as an ordinary or partial differential equation which depends on whether only ordinary derivatives are involved or partial derivatives are involved. Classification of ordinary and partial equations
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