Find the differential equation of family of curves y=ex(Acosx+Bsinx) where A and B are arbitrary constants.
y=ex(Acosx+Bsinx)
y1=ex(−Asinx+Bcosx)+ex(Acosx+Bsinx)
y1=ex(A(cosx−sinx)+B(cosx+sinx))
y2=ex(A(−sinx−cosx)+B(sinx+cosx))+ex(A(cosx−sinx)+B(cosx+sinx))
y2=ex(A(−2sinx))+B(2cosx))
y2=2ex(Bcosx−Asinx)
As, y+y22=y1
y2−2y1+2y=0