## anonymous 4 years ago Suppose that y1(t) and y2(t) are both solutions to the differential equation dy/dt= a(t)y + b(t). Write down a linear differential equation satisfied by y1(t) + y2(t).

$y'_1=a(t)y_1+b(t)$$y'_2=a(t)y_2+b(t)$$\sum\quad\Rightarrow\quad y'_1+y'_2=a(t)y_1+a(t)y_2+2b(t)$$(y_1+y_2)'=a(t)(y_1+y_2)+2b(t)\quad,\quad z=y_1+y_2$$z'=a(t)z+2b(t)$