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  • Explain solution RD Sharma class 12 chapter Differential Equations exercise 21.7 question 28 maths

Explain solution RD Sharma class 12 chapter Differential Equations exercise 21.7 question 28 maths

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Answer: y=\log \left(c(1+y)\left(e^{x}+1\right)\right)

Hint: Separate the terms of x and y and then integrate them.

Given: y\left(1+e^{x}\right) d y=(y+1) e^{x} d x

Solution: y\left(1+e^{x}\right) d y=(y+1) e^{x} d x

        \frac{y d y}{(y+1)}=\frac{e^{x}}{\left(1+e^{x}\right)} d x

          Integrating both sides

        \begin{aligned} &\Rightarrow y-\log |y+1|=\log \left|e^{x}+1\right|+\log c \\\\ &\Rightarrow y=\log |y+1|+\log \left|e^{x}+1\right|+\log c \\\\ &y=\log \left(c(1+y)\left(e^{x}+1\right)\right) \end{aligned}

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