W =
cosx −senx
W1 =
senx = cos2 x + sen2 x = 1 cosx
0 senx = −senxcos2 x cos2 x cosx cosx −senx
W2 =
0 = cos3 x cos2 x
De nimos u1 , u2 −senxcos2 x = −senxcos2 x 1 " # ´ cos3 x cos3 x 2 u1 = − senxcos xdx = − − = 3 3 u01 =
u02 = u2 =
´
cos3 x = cos3 x 1
cos3 xdx = senx −
sen3 x 3
! cos3 x sen3 x (cosx) + senx − (senx) 3 3
yp = u1 y1 + u2 y2 =
yp =
cos4 x sen4 x + sen2 x − 3 3
y(x) = c1 cosx + c2 senx +
sen4 x cos4 x + sen2 x − 3 3
4.y00 − y = cosh x Ecuacion homogenea asociada y00 − y = 0 m2 − 1 = 0 √ m2 = 1; m1,2 = ± 1 = ±1 yh = c1 ex + c2 e−x
De nimos y1 , y2 y1 = ex ; y10 = ex y2 = e−x ; y20 = −e−x
Calculamos los Wronskianos: 24