What is the solution of the equationln(dydx)+x=0? | Filo
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Differential Equations

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What is the solution of the equationln(dydx)+x=0?

  1. y+ex=c
  2. y−e−x=c
  3. y+e−x=c
  4. y−ex=c
Correct Answer: Option(c)
Solution: [c] Consider the given differential equation ln(dydx)+x=0⇒ln(dydx)=−x ⇒dydx=e−x On separating the variables, we get dy=e−xdx, On integrating both sides, we get ∫dy=∫e−xdx ⇒y=e−x−1+C=−e−x+C⇒y+e−x=C
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