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  • Provide Solution For R.D.Sharma Maths Class 12 Chapter 21 Differential Equations Exercise Revision Exercise Question 3 Sub Question 4 Maths Textbook Solution.

Provide Solution For R.D.Sharma Maths Class 12 Chapter 21 Differential Equations Exercise  Revision Exercise Question 3 Sub Question 4 Maths Textbook Solution.

Answers (1)

Answer:

                Verified

Hint:

Find the first derivative of given function and put value in differential equation

Given:

        y=\sqrt{1+x^{2}}

        {y}'=\frac{xy}{1+x^{2}}

Solution:

            \begin{aligned} &y^{\prime}=\frac{d y}{d x}=\frac{1}{2} \frac{1}{\sqrt{1+x^{2}}} \cdot 2 x \ldots \text { using chain rule } \\ &y^{\prime}=\frac{x}{\sqrt{1+x^{2}}} \end{aligned}

Put in differential equation,

                {y}'=\frac{xy}{1+x^{2}}

LHS=      \frac{x}{\sqrt{1+x^{2}}}

Multiply and divide by \sqrt{1+x^{2}}

                 \begin{aligned} &=\frac{x}{\sqrt{1+x^{2}}} \times \frac{\sqrt{1+x^{2}}}{\sqrt{1+x^{2}}} \\ &=\frac{x \sqrt{1+x^{2}}}{\left(1+x^{2}\right)} \end{aligned}

Where,y=\sqrt{1+x^{2}}

Therefore, LHS= \frac{xy}{1+x^{2}} RHS..Hence verified.

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