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\begin{align} y= \sqrt{1+x^2} : y^{'}=\frac{xy}{1+x^2}\e...

egin{align} y= sqrt{1+x^2} :&nbs | Class 12 Mathematics Chapter Differential Equations, Differential Equations NCERT Solutions

Question:

\begin{align} y= \sqrt{1+x^2} : y^{'}=\frac{xy}{1+x^2}\end{align}

Answer:

\begin{align} y= \sqrt{1+x^2}\end{align}

Differentiating both sides of the equation with respect to x, we get:

\begin{align} y^{'}=\frac{d}{dx}\left(\sqrt{1+x^2} \right)\end{align}

\begin{align} y^{'}=\frac{1}{2\sqrt{1+x^2}}\frac{d}{dx}\left(1+x^2\right)\end{align}

\begin{align} y^{'}=\frac{2x}{2\sqrt{1+x^2}}\end{align}

\begin{align} y^{'}=\frac{x}{\sqrt{1+x^2}}\end{align}

\begin{align}\Rightarrow y^{'}=\frac{x}{\sqrt{1+x^2}}\frac{\sqrt{1+x^2}}{\sqrt{1+x^2}}\end{align}

\begin{align}\Rightarrow y^{'}=\frac{x}{1+x^2}{\sqrt{1+x^2}}\end{align}

\begin{align}\Rightarrow y^{'}=\frac{x}{1+x^2}{y}\end{align}

\begin{align}\Rightarrow y^{'}=\frac{xy}{1+x^2}\end{align}

∴ L.H.S. = R.H.S.

Hence, the given function is the solution of the corresponding differential equation.

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Popular questions of class 12 Mathematics

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Reference examples and data from the chapter when answering questions about Differential Equations.
Review previous year question papers to get an idea of how such questions may be framed in exams.
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Welcome to the NCERT Solutions for Class 12 Mathematics - Chapter . This page offers a step-by-step solution to the specific question from Excercise 2 , Question 4: egin{align} y= sqrt{1+x^2} : y^{'}=frac{xy}{1+x^2}end{align}....

egin{align} y= sqrt{1+x^2} :&nbs | Class 12 Mathematics Chapter Differential Equations, Differential Equations NCERT Solutions

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egin{align} y= sqrt{1+x^2} :&nbs | Class 12 Mathematics Chapter Differential Equations, Differential Equations NCERT Solutions