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  • Need solution for RD Sharma maths class 12 chapter Differential Equations exercise 21.7 question 27

Need solution for RD Sharma maths class 12 chapter Differential Equations exercise 21.7 question 27

Answers (1)

Answer: -\sqrt{1-y^{2}}=\sqrt{1-x^{2}}+c \text { or } \sqrt{1-x^{2}}+\sqrt{1-y^{2}}=c

Hint: You must know about the rules of solving differential equation and integration

Given: x \sqrt{1-y^{2}} d x+y \sqrt{1-x^{2}} d y=0

Solution:

        y \sqrt{1-x^{2}} d y=-x \sqrt{1-y^{2}} d x

        \int \frac{y}{\sqrt{1-y^{2}}} d y=\int \frac{-x}{\sqrt{1-x^{2}}} d x

        We know \frac{d}{d x}\left(\sqrt{1-x^{2}}\right)=\frac{-x}{\sqrt{1-x^{2}}}

        Integration of \frac{-x}{\sqrt{1-x^{2}}} d x=\sqrt{1-x^{2}}

        Similarly Integration of \frac{y}{\sqrt{1-y^{2}}} d y=-\sqrt{1-y^{2}}     

        \begin{aligned} &\Rightarrow-\sqrt{1-y^{2}}=\sqrt{1-x^{2}}+c \\\\ &\Rightarrow-\sqrt{1-y^{2}}-\sqrt{1-x^{2}}=c \\\\ &\Rightarrow-\left[\sqrt{1-x^{2}}+\sqrt{1-y^{2}}\right]=c \end{aligned}

        \begin{aligned} &\Rightarrow \sqrt{1-x^{2}}+\sqrt{1-y^{2}}=-c \\\\ &\Rightarrow \sqrt{1-x^{2}}+\sqrt{1-y^{2}}=c \end{aligned}

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