例6设y= e" sin bx(a,b为常数,求ym 解y′= ae" sin bx+ be cos bx e(asin bx t b cos bx) =e·a2+b2sin(bx+φ)(q= arctan y=Na+b ae sin(bx +(p)+be cos(bx+p) Na+be.va+b sin(bx+2p) b y(n=(a+b2)2.ea sin (bx+no ((=arctan例 6 sin ( , ), . ax (n) 设 y = e bx a b为常数 求y 解 y ae bx be bx ax ax  = sin + cos e (a sin bx bcos bx) ax = + sin( ) ( arctan ) 2 2 ab e a b bx ax =  + +   = [ sin( ) cos( )] 2 2 y  = a + b  ae bx +  + be bx +  ax ax sin( 2 ) 2 2 2 2 = a + b  e  a + b bx +  ax  ( ) sin( ) ( ) 2 2 2 y = a + b  e bx + n ax n n ( arctan ) ab  =