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  • Explain solution for RD Sharma Class 12 Chapter 21 Differential Equation Exercise Multiple choice Question Question 51 maths textbook solution.

Explain solution for  RD Sharma Class 12 Chapter 21 Differential Equation Exercise Multiple choice Question Question 51 maths textbook solution.

Answers (1)

Answer : \text { (d) } \frac{1}{\sqrt{1-y^{2}}}

Hint : The equation is linear in x

Given : \left(1-y^{2}\right) \frac{d y}{d x}+y x=a y,(-1<y<1)

Explanation : Divide on both ides by 1-y^{2}

\Rightarrow \frac{d y}{d x}+\frac{x}{1-y^{2}} y=\frac{a y}{1-y^{2}}

So, the equation becomes linear in x

\begin{aligned} &I F=e^{\int \frac{y}{1-y^{2}} d y} \\ &\text { Let } 1-y^{2}=t \\ &\Rightarrow-2 y d y=d t \\ &\Rightarrow y d y=-\frac{d t}{2} \\ &\Rightarrow I F=e^{-\frac{1}{2} \int \frac{d t}{t}} \end{aligned}

               \begin{aligned} &=e^{-\frac{1}{2} \log t} \\ &=e^{\log t^{-\frac{1}{2}}} \\ &=t^{-\frac{1}{2}} \\ &=\frac{1}{\sqrt{t}} \\ &=\frac{1}{\sqrt{1-y^{2}}} \end{aligned}

 

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