COMEDK · Maths · 32. Differential Equations
The solution of the differential equation \(\dfrac{d y}{d x}=e^{x+y}+x^2 e^y\) is
- A \(e^{x-y}+\dfrac{x^3}{3}=c\)
- B \(e^x-e^{-y}+\dfrac{x^3}{3}=c\)
- C \(e^x+e^{-y}+\dfrac{x^3}{3}=c\)
- D \(e^x-e^{-y}=\dfrac{x^3}{3}+c\)
Answer & Solution
Correct Answer
(C) \(e^x+e^{-y}+\dfrac{x^3}{3}=c\)
Step-by-step Solution
Detailed explanation
The given differential equation is \(\dfrac{dy}{dx} = e^{x+y} + x^2 e^y\). Factoring out \(e^y\) from the right side, we get \(\dfrac{dy}{dx} = e^y(e^x + x^2)\). Separating the variables, we have \(\dfrac{dy}{e^y} = (e^x + x^2) dx\), which can be written as…
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