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Need solution for RD Sharma maths Class 12 Chapter 21 Differential Equation Exercise Revision Exercise (RE) Question 65 Subquestion (ii) textbook solution.

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Answer : \cos \left(\frac{y-1}{x}\right)=a

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

Given           : \cos \left(\frac{d y}{d x}\right)=a

Solution        : \cos \left(\frac{d y}{d x}\right)=a

                     \begin{aligned} &\frac{d y}{d x}=\cos ^{-1} a \\ &d y=\cos ^{-1} a d x \end{aligned}

Integrating both sides,

           \begin{aligned} &\int d y=\int \cos ^{-1} a d x \\ &\int d y=\cos ^{-1} a \int d x \\ &y=x \cos ^{-1} a+c \end{aligned}

Now, x=0,y=1

Therefore, 1=0+C



\begin{aligned} &y=x \cos ^{-1} a+1 \\ &\cos \left(\frac{y-1}{x}\right)=a \end{aligned}

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