​ The solution of the DE dy/dx = e^x+y is ​

Question

The solution of the DE \(\frac{dy}{dx}\) = e^x+y is

A. e^x + e^y = c

B. e^x - e^-y = c

C. e^x + e^-y = c

D. None of these

Answer 1

Given, \(\frac{dy}{dx}\) = e^x+y

\(\frac{dy}{dx}\) = e^xe^y

e^-y dy = e^x dx

On integrating on both sides, we get

 - e^-y + c₁ e^x +c₂

e^-y + e^x = c

Conclusion: Therefore, e^-y + e^x = c is the solution of \(\frac{dy}{dx} \) e^x+y