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; ...

You visited us 6 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

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

Open in App

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

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

Suggest Corrections

Similar questions

Q. Verify that y = − x − 1 is a solution of the differential equation (y − x) dy − (y² − x²) dx = 0.

Q. Verify that

a x^{2} + b y^{2} = 1

is a solution of the differential equation

x (y y_{2} + y_{1}^{2}) = y y_{1}

y = a e^{- 1 / x} + b

is a solution of the differential equation

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

when

Q. Solution of differential equation

\frac{d y}{d x} + \frac{y}{1 + x^{2}} = \frac{e^{t a n^{- 1} x}}{1 + x^{2}}

For the following question verify that the given function (explicit or implicit) is a solution of the corresponding differential equation.

$y = \sqrt{1 + x^{2}} a n d y^{'} = \frac{x y}{1 + x^{2}}$

Join BYJU'S Learning Program

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

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