If (y=e^ -x x ) and (y₄+k y=0 ), where (y₄= d^4 y d x^4 ), then (k= )

Step-by-step solution

Let (y=e^ -x x ) ( aligned & y ₁=-e^ -x x-e^ -x x=-e^ -x x-y & y₂=-e^ -x x+e^ -x x-y₁ & y₂=-y-y₁+e^ -x x=-2 (y+y₁ ) & y₃=-2 (y₁+y₂ )=-2 (e^ -x x-y ) & y₄=4 y₁+2 y₂=4 y₁-4 y-4 y₁ or y₄+4 y=0 & k=4 aligned )