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Home » Mark (√) against the correct answer in the following: The solution of the DE is A. B. C. D. None of these
Mark (√) against the correct answer in the following: The solution of the DE \frac{d y}{d x}=\mathrm{e}^{x+y} is
A. \mathrm{e}^{\mathrm{x}}+\mathrm{e}^{\mathrm{y}}=\mathrm{C}
B. \mathrm{e}^{\mathrm{x}}-\mathrm{e}^{-\mathrm{y}}=\mathrm{C}
C. \mathrm{e}^{\mathrm{x}}+\mathrm{e}^{-\mathrm{y}}=\mathrm{C}
D. None of these
CBSE | Class 12 | Linear Differential Equations | Maths | RS Aggarwal
Mark (√) against the correct answer in the following: The solution of the DE \frac{d y}{d x}=\mathrm{e}^{x+y} is
A. \mathrm{e}^{\mathrm{x}}+\mathrm{e}^{\mathrm{y}}=\mathrm{C}
B. \mathrm{e}^{\mathrm{x}}-\mathrm{e}^{-\mathrm{y}}=\mathrm{C}
C. \mathrm{e}^{\mathrm{x}}+\mathrm{e}^{-\mathrm{y}}=\mathrm{C}
D. None of these

Solution:

\begin{array}{c} \frac{d y}{d x}=e^{x+y} \\ \frac{d y}{d x}=e^{x} e^{y} \\ e^{-y} d y=e^{x} d x \end{array}
On integrating on both sides, we get
\begin{array}{c} -e^{-y}+c_{1}=e^{x}+c_{2} \\ e^{-y}+e^{x}=c \end{array}
Therefore, e^{-y}+e^{x}=c is the solution of \frac{d y}{d x}=e^{x+y}

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