A 53-year-old presents after admission to the general medical/surgical hospital ward with a chief complaint of shortness of breath on exertion. She reports that she was seen for similar symptoms previously at her primary care physician’s office six months ago. At that time, she was diagnosed with acute bronchitis and treated with bronchodilators, empiric antibiotics, and a short course oral steroid taper. This management did not improve her symptoms, and she has gradually worsened over six months. Her vital signs are ******. She takes Lasix 40mg every day and states that she has gained 10 pounds since this time last year. You notice that her tactile fremitus is increased indicating.
Obtain the general solution of the following DEs: i. y′′′ + y′′ − 4y′ + 2y = 0 ii. y(4) + 4y(2) = 0 iii. x(x − 2)y′′ + 2(x − 1)y′ − 2y = 0; use y1 = (1 − x) iv. y′′ − 4y = sin2(x) v. y′′ − 4y′ + 3y = x ; use y1 = e3x vi. y′′ + 5y′ + 6y = e2xcos(x) vii. y′′ + y = sec(x) tan(x)
Obtain the general solution of the following DEs: i. y′′′ + y′′ − 4y′ + 2y = 0 ii. y(4) + 4y(2) = 0 iii. x(x − 2)y′′ + 2(x − 1)y′ − 2y = 0; use y1 = (1 − x) iv. y′′ − 4y = sin2(x) v. y′′