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  • Please solve RD Sharma Class 12 Chapter 21 Differential Equation Exercise Multiple Choice Question Question 27 maths textbook solution.

Please solve RD Sharma Class 12 Chapter 21 Differential Equation Exercise Multiple Choice Question Question 27 maths textbook solution.

Answers (1)

Answer : (d)(x+C) e^{x+y}+1=0

Hint: Substitute x+y=t and separate x and t terms.

Given : \frac{d y}{d x}+1=e^{x+y}                   .....(i)

Explanation : Let y+x=t

Differentiate with respect to x

\Rightarrow \frac{d y}{d x}+1=\frac{d t}{d x}

Put in (i) we get

\begin{aligned} &\Rightarrow \frac{d t}{d x}=e^{t} \\ &\Rightarrow \frac{d t}{e^{t}}=d x \\ &\Rightarrow e^{-t} d t=d x \end{aligned}

Integrate both sides

\begin{aligned} &\Rightarrow-e^{-t}=x+C \\ &\Rightarrow-e^{-(x+y)}=x+C \end{aligned}

\begin{aligned} &\Rightarrow-1=(x+C) e^{x+y} \\ &\Rightarrow(x+C) e^{x+y}+1=0 \end{aligned}

 

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