Question

3. Consider the ODE: 22+3 +5x2 = sin nt A) Is this ODE linear or nonlinear? Use the superposition property to support your conclusion. If nonlinear, state term(s) that make it nonlinear. B) Is this ODE time varying or time-invariant? If time varying, state term(s) that make it time varying. 4. Consider the ODE: 23+3xx +5t2x = 5t A) Is this ODE linear or nonlinear? Use the superposition property to support your conclusion. If nonlinear, state term(s) that make it nonlinear. B) Is this ODE time varying or time-invariant? If time varying, state term(s) that make it time varying. It can be shown that the ODE for a mass m suspended on a massless string of length L under gravity g, is +sin 0 0 where 0 is the angle that the string makes with the vertical direction. Answer the following 5. A) Is this ODE time varying or time-invariant? If time varying, state term(s) that make it time varying. B) What term makes this a nonlinear ODE? C) Write the linear ODE that results from assuming 0<< 1.

Answer 1

sis t 2i+ 3n t 5t - ODE he ODE js nGn-linaor dua ta the fresenca of 5xterm lincari ty causes linsor thefor AB Linaar unear b non-inaer dieren ia 522= sinTt But Sum hem auperferition due tern sinTt 9t is time-voruant