The differential equation found by the elimination of the ar... | MATH - FORMATION OF DIFFERENTIAL EQUATIONS | SolveeIt | Solveeit

Today, August 20

Question

The differential equation found by the elimination of the arbitrary constant K from the equation $y = ( x + K ) e ^ { - x }$ is

A

$\frac { d y } { d x } - y = e ^ { - x }$

B

$\frac { d y } { d x } - y e ^ { x } = 1$

C

$\frac { d y } { d x } + y e ^ { x } = 1$

D

$\frac { d y } { d x } + y = e ^ { - x }$

Answer

$\frac { d y } { d x } + y = e ^ { - x }$

Explanation

Solution

$y = ( x + K ) e ^ { - x }$ ⇒ $\frac { d y } { d x } = - ( x + K ) e ^ { - x } + e ^ { - x }$

⇒ $\frac { d y } { d x } = - y + e ^ { - x }$ ⇒ $\frac { d y } { d x } + y = e ^ { - x }$ .