solve-xy-2y-xy-0-with-initial-conditions-y-o-1-and-y-1-0-

Question Number 82476 by abdomathmax last updated on 21/Feb/20

s o l v e {x y}^{^{″}} + 2 y^{^{'}} + x y = 0 w i t h i n i t i a l c o n d i t i o n s

y (o) = 1 a n d y^{^{'}} (1) = 0

Answered by mind is power last updated on 21/Feb/20

z = x y

\Rightarrow z^{'} = y + {x y}^{'}

z^{″} = 2 y^{'} + {x y}^{″}

{x y}^{″} + 2 y^{'} + x y = 0

\Rightarrow z^{″} + z = 0