Misc 1 - For each differential equation, indicate order, degree

Misc 1 For each of the differential equation given below , indicate its order and degree 𝑖𝑓 𝑑𝑒𝑓𝑖𝑛𝑒𝑑﷯ (i) 𝑑﷮2﷯𝑦﷮𝑑 𝑥﷮2﷯﷯+5𝑥 𝑑𝑦﷮𝑑𝑥﷯﷯﷮2﷯−6𝑦= log﷮𝑥﷯ 𝑑﷮2﷯𝑦﷮𝑑 𝑥﷮2﷯﷯+5𝑥 𝑑𝑦﷮𝑑𝑥﷯﷯﷮2﷯−6𝑦= log﷮𝑥﷯ y” + 5x 𝑦′﷯﷮2﷯−6𝑦= log﷮𝑥﷯ Highest order of derivative = 2 ∴ Order = 2 Since, power of y” is 1 ∴ Degree = 1 Misc 1 For each of the differential equation given below , indicate its order and degree 𝑖𝑓 𝑑𝑒𝑓𝑖𝑛𝑒𝑑﷯ (ii) 𝑑𝑦﷮𝑑𝑥﷯﷯﷮3﷯−4 𝑑𝑦﷮𝑑𝑥﷯﷯﷮2﷯+7𝑦= sin﷮𝑥﷯ 𝑑𝑦﷮𝑑𝑥﷯﷯﷮3﷯−4 𝑑𝑦﷮𝑑𝑥﷯﷯﷮2﷯+7𝑦= sin﷮𝑥﷯ y﷮′﷯﷯﷮3﷯− 4 𝑦′﷯﷮2﷯ 7𝑦= sin﷮𝑥﷯ Highest order of derivative = 1 ∴ order = 1 Since, power of y’ is 3, Degree = 3 Misc 1 For each of the differential equation given below , indicate its order and degree 𝑖𝑓 𝑑𝑒𝑓𝑖𝑛𝑒𝑑﷯ (iii) 𝑑﷮4﷯𝑦﷮𝑑 𝑥﷮4﷯﷯−𝑠𝑖𝑛 𝑑﷮3﷯𝑦﷮𝑑 𝑥﷮3﷯﷯﷯=0 𝑑﷮4﷯𝑦﷮𝑑 𝑥﷮4﷯﷯−𝑠𝑖𝑛 𝑑﷮3﷯𝑦﷮𝑑 𝑥﷮3﷯﷯﷯=0 y﷮′′′′﷯−𝑠𝑖𝑛 𝑦′′′﷯0 Highest order of derivative = 4 ∴ Order = 4 Since 𝑦“ is in sin (𝑦“), It is not 𝑎 polynomial equation in derivatives, Thus, degree is not defined.