Question

1. Use the method of variation of parameters to find a particular solution to the equation below. Then use your particular solution to find a general solution to the equation. -10et y" – 2y' + y = 72 +4

Answer 1

Solution y" - 2y' + y = lo et t² + 4 Auxillary equation : m? - 2m + 1 = 0 (m - 2)? = o 1 I СЕ (c + C₂ t). et t yi of Wo= -loe stet and - Y2 + 2 + 4 et tet Wronkian determinant, 41 Ya Y2 42 1 - The et (t+1) ē (#+1) - ett e t 2t 1) 2 t W = e

PI = -y, Sy wodt + yo Swe de Slot t te dt tet lo dt t²4 t? +4 te (10) tant t **(1) # 11 loet en (x²+4) 2 2 t t stet tan =. se enlt²+ 4) o sé [ln (4+4) - † fan' (:)] 다. CF + PI general solution y (+) = (5,+cz t)e+ + set [Ance'ta) - £ lon(!)] Answer