What is the main difference between solutions of linear ODEs

What is the main difference between solutions of linear ODE\'s and nonlinear ODE\'s assuming the linear! non linear ODE satisfy the conditions for existence uniqueness of theorems 2.4.1 and 2.4.2 If the functions p & g are conditions on an open interval I: alpha

Solution

Therefore are numerous differences between the linear and nonlinear differential equations. For instance, theorems describing uniqueness and existence of solutions and respective domains are quite different for linear and non-linear differential equations.

Main differenece between the solutions of linear and nonlinear differential equations is that solutions to linear equations can be expressed in terms of general solutions, but it is not necessarily true for non-linear equations. Furthermore, solutions to linear differential equations can be explicitly defined, however, for non-linear differential equations solutions cannot be gauranteed to have explicitly defined.