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  • Provide solution for RD Sharma maths class 12 chapter Differential Equations exercise 21.7 question 30

Provide solution for RD Sharma maths class 12 chapter Differential Equations exercise 21.7 question 30

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Answer: \log (1+y)=x-\frac{x^{2}}{2}+c

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

Given: \frac{d y}{d x}=1-x+y-x y

Solution: \frac{d y}{d x}=1-x+y-x y

        \begin{aligned} &\frac{d y}{d x}=(1-x)(1+y) \\\\ &\frac{d y}{(1+y)}=(1-x) d x \\\\ &\int \frac{d y}{(1+y)}=\int 1 d x-\int x d x \\ \end{aligned}

        \log (1+y)=x-\frac{x^{2}}{2}+c

 

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