1.

Find the general solution of the following differential equation:\(\frac{dx}{dy} = e^{x -y}+ x^2e^{-y}\)

Answer»

\(\frac{dx}{dy} = e^{x -y}+ x^2e^{-y}\)

⇒ \(dy = (e^{x-y} + x^2e^{-y})dx\)

⇒ \(dy = \frac{(e^x + x^2) }{e^y}dx\)

⇒ \(e^y \, dy = (e^x + x^2)dx\)

⇒ \(\int e^y dy = \int (e^x + x^2)dx\)

\(\therefore \,e^y = e^x + \frac{x^3}{3}+ C\), which is the required solution.


Discussion

No Comment Found

Related InterviewSolutions