Verify whether y-1-x2 is a solution of the differential equation y-x-1-x2

y=√(1+x^2) squaring both sides, we get y^2=1+x^2 2ydydx=2x ⇒dydx=xy Where y=√(1+x^2) ⇒dydx=x√(1+x^2) #160; ...

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Standard XII

Mathematics

General Solution of a Differential Equation

Verify whethe...

Question

Verify whether $y = \sqrt{1 + x^{2}}$ is a solution of the differential equation $y^{'} = \frac{x}{\sqrt{1 + x^{2}}}$

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Solution

$y = \sqrt{1 + x^{2}}$

squaring both sides, we get

$y^{2} = 1 + x^{2}$

$2 y \frac{d y}{d x} = 2 x$

$\Rightarrow \frac{d y}{d x} = \frac{x}{y}$

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

$\Rightarrow \frac{d y}{d x} = \frac{x}{\sqrt{1 + x^{2}}}$

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Verify whether y=√1+x2 is a solution of the differential equation y′=x√1+x2

y=√1+x2squaring both sides, we gety2=1+x22ydydx=2x⇒dydx=xyWhere y=√1+x2⇒dydx=x√1+x2

Verify whether $y = \sqrt{1 + x^{2}}$ is a solution of the differential equation $y^{'} = \frac{x}{\sqrt{1 + x^{2}}}$

$y = \sqrt{1 + x^{2}}$

squaring both sides, we get

$y^{2} = 1 + x^{2}$

$2 y \frac{d y}{d x} = 2 x$

$\Rightarrow \frac{d y}{d x} = \frac{x}{y}$

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

$\Rightarrow \frac{d y}{d x} = \frac{x}{\sqrt{1 + x^{2}}}$