The solution of the equation \( dy dx = e x + y + x 2e y\) is

\[ dy/dx = e x - y + x 2 e -y \] \[ dy = ( e x - y + x 2 e -y ) dx \] \[ dy = e x + x 2/e y dx \] \[ e y dy = ( e x + x 2 ) dx \] \[ ∈t e y dy = ∈t (e x + x 2) dx \] \[ e y = e x + x 3/3 + C \] Thus, the required solution is: \[ e y = e x + x 3/3 + C \]

The solution of the equation <span... - Solved

\( dy dx = e x + y + x 2e..." - Step-by-step solution, answer key, and detailed explanation on MCA Prep."> \( dy dx = e x + y + x 2e..." - Step-by-step solution, answer key, and detailed explanation on MCA Prep." /> \( dy dx = e x + y + x 2e..." - Step-by-step solution, answer key, and detailed explanation on MCA Prep." />

Home Rankers PYQ Blogs Pricing About Contact

Question 48

Mathematics Matrices Hard

The solution of the equation \(\frac {dy}{dx} = e^{x + y} + x^2e^y\) is

(A) \(e^{x - y} + \frac {x^3} 3 + c\)

(B) \(e^{x} + e^{-y} + \frac {x^3} 3 = c\)

(C) \(e^{x} - e^{-y} = \frac {x^3} 3 + c\)

(D) None

✓ Correct Answer: Option B Verified Solution

📘 Step-by-Step Solution & Detailed Explanation:

\[ \frac{dy}{dx} = e^{x - y} + x^2 e^{-y} \] \[ \Rightarrow dy = \left( e^{x - y} + x^2 e^{-y} \right) dx \] \[ \Rightarrow dy = \frac{e^x + x^2}{e^y} dx \] \[ \Rightarrow e^y dy = \left( e^x + x^2 \right) dx \] \[ \Rightarrow \int e^y dy = \int (e^x + x^2) dx \] \[ \Rightarrow e^y = e^x + \frac{x^3}{3} + C \] Thus, the required solution is: \[ e^y = e^x + \frac{x^3}{3} + C \]

← Previous Question Our Rankers Next Question →