Question

work and label your answers clearly. 1. Classify the following ODEs. Include the order, homogeneous or hon-homogeneous, linear or non-linear, and ables also state the independent and dependent vari- 32+5x + z = 0 10%, + 5tr = 15 12v2 9 dr

Answer 1

Given that 3x + 5 x + x = 0 x = d^2 x/dt^2 x = dx/dt substitute the x and x in equation 1 3 d^2 x/dt^2 + 5 dx /dt + x = 0 from the above equation it is clear that it is second order linear differential equation it is also a homogenous equation order height order derivative - 2 in equation 1 degree: - power of the highest order derivative = 1 dependent variable = x independent variable = b 10 dx/dt + 5 t x = 15 10 dx/dt + 5 tx = 15 from equation 1 it is clear that It is the first order linear differential equation which is non - homogeneous equation order = 1 degree = 1 dependent variable = x independent variable = t 4 v + 1 v^2 = 9 It is non-homogeneous first order linear differential equation dependent variable = v independent variable = t order = 1 degree = 1 a d^2 x/d t^2 + b dx/dt = -cx we