The solution of the differential equation \(\rm dy\over dx \) = ex -

1.	The solution of the differential equation \(\rm dy\over dx \) = ex - y is1. e-y + e-x = c2. e-y - ex = c3. ey - ex = c4. ey + ex = c
Answer» Correct Answer - Option 3 : ey - ex = c Concept: The solution of the differential equation can be found out by separating the variables and integrating them individually. Calculation: The given differential equation is \(\rm {dy\over dx} = e^{x-y}\) ⇒ \(\rm {dy\over dx} = {e^x\over e^y}\) ⇒ e^y dy = e^x dx Integrating both sides ⇒ ∫ ey dy = ∫ ex dx ⇒ ey = ex + c ⇒ ey - ex = c

The solution of the differential equation \(\rm dy\over dx \) = ex - y is1. e-y + e-x = c2. e-y - ex = c3. ey - ex = c4. ey + ex = c

Answer» Correct Answer - Option 3 : ey - ex = c

Concept:

The solution of the differential equation can be found out by separating the variables and integrating them individually.

Calculation:

The given differential equation is

\(\rm {dy\over dx} = e^{x-y}\)

⇒ \(\rm {dy\over dx} = {e^x\over e^y}\)

⇒ e^y dy = e^x dx

Integrating both sides

⇒ ∫ ey dy = ∫ ex dx

⇒ ey = ex + c

⇒ ey - ex = c

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The solution of the differential equation \(\rm dy\over dx \) = ex - y is1. e-y + e-x = c2. e-y - ex = c3. ey - ex = c4. ey + ex = c

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