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

Class 12

Math

Calculus

Differential Equations

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150

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
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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