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  • Need solution for RD Sharma maths Class 12 Chapter 21 Differential Equation Exercise Revision Exercise (RE) Question 64 Subquestion (v) textbook solution.

Need solution for RD Sharma maths Class 12 Chapter 21 Differential Equation Exercise Revision Exercise (RE) Question 64 Subquestion (v) textbook solution.

Answers (1)

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

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

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

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

                          \frac{d y}{d x}=\sin ^{-1} x\; dx

Integrating  both sides

                    \int d y=\int 1 \times \sin ^{-1} x d x

Integrating by parts,

 Put               \begin{aligned} \int d y &=\sin ^{-1} x \int 1 d x-\int\left[\frac{d}{d x}\left(\sin ^{-1} x\right) \int 1 d x\right] d x \\ y &=x \sin ^{-1} x-\int \frac{x}{\sqrt{1-x^{2}}} d x \\ t^{2} &=1-x^{2}, \text { and differentiate we get } \end{aligned}

                             \begin{gathered} 2 t d t=-2 x d x \\ \Rightarrow-t d t=x d x \end{gathered}

Therefore,    

                            \begin{aligned} &y=x \sin ^{-1} x+\int d t \\ &y=x \sin ^{-1} x+t+c \\ &y=x \sin ^{-1} x+\sqrt{1-x^{2}}+c \end{aligned}

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