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  • Provide Solution For R.D.Sharma Maths Class 12 Chapter 21 Differential Equations Exercise Revision Exercise Question 3 Sub Question 5 Maths Textbook Solution.

Provide Solution For  R.D.Sharma Maths Class 12 Chapter 21 Differential Equations Exercise  Revision Exercise Question 3 Sub Question 5 Maths Textbook Solution.

Answers (1)

Answer:

                Verified

Hint:

You must firstly solve the first derivative and put value in differential equation

Given:

        y=x\sin x

         {xy}'=y+x\sqrt{x^{2}-y^{2}}

Solution:

            {y}'=\frac{dy}{dx}=\sin x+x\cos x.....using \; \; product\: \: rule

Put in differential equation {xy}'=y+x\sqrt{x^{2}-y^{2}}

LHS=x y^{\prime}=x(\sin x+x \cos x)

                           =x \sin x+x^{2} \cos x

\begin{aligned} &\text { RHS }=y+x \sqrt{x^{2}-y^{2}}\\ &=x \sin x+x \sqrt{x^{2}-(x \sin x)^{2}}\\ &\begin{aligned} &=x \sin x+x \sqrt{x^{2}\left(1-\sin ^{2} x\right)} \\ &=x \sin x+x^{2} \sqrt{\cos ^{2} x} \end{aligned} \quad\left[\begin{array}{l} \because \sin ^{2} x+\cos ^{2} x=1 \\ \cos ^{2} x=1-\sin ^{2} x \end{array}\right]\\ &=x \sin x+x^{2} \cos x \end{aligned}

LHS=RHS

Hence verified

Posted by

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