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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}=2^{x+y} is
A. 2^{x}+2^{y}=C
B. 2^{x}+2^{-y}=C
C. 2^{x}-2^{-y}=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}=2^{x+y} is
A. 2^{x}+2^{y}=C
B. 2^{x}+2^{-y}=C
C. 2^{x}-2^{-y}=C
D. None of these

Solution:

\begin{array}{c} \frac{d y}{d x}=2^{x} 2^{y} \\ 2^{-y} d y=2^{x} d x \end{array}
\frac{d y}{d x}=2^{x+y}
On integrating on both sides, we get
\begin{array}{c} -\frac{2^{-y}}{\log 2}+c_{2}=\frac{2^{x}}{\log 2} \\ 2^{x}+2^{-y}=c_{3} \log 2 \\ 2^{x}+2^{-y}=c \end{array}
Therefore 2^{x}+2^{-y}=c is the solution of \frac{d y}{d x}=2^{x+y}

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