Let y - yx be the solution of the differential equation ex-1-y2 dx-yxdy-0- y1-1- Then the value of y32 is equal to

E^x √(1 y^2)dx= yxdy ⇒∫ xe^xdx=∫ y√(1 y^2)dy ⇒ xe^x e^x=√(1 y^2)+c y(1)= 1 ⇒ 0=0+c⇒ c=0 ∴ xe^x e^x=√(1 y^2) for y(3) put x=3 3e^3 e^3=√(1 y^2) ⇒ 4e^6=1 y^2 ⇒ (y ...

You visited us 2 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Integrating Factor

Let y = yx be...

Question

Let $y = y (x)$ be the solution of the differential equation $e^{x} \sqrt{1 - y^{2}} d x + (\frac{y}{x}) d y = 0,$ $y (1) = - 1.$ Then the value of $(y (3))^{2}$ is equal to

1 + 4 e^{6}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

1 - 4 e^{6}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

1 - 4 e^{3}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

1 + 4 e^{3}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B $1 - 4 e^{6}$
$e^{x} \sqrt{1 - y^{2}} d x = - \frac{y}{x} d y$
$\Rightarrow \int x e^{x} d x = \int \frac{- y}{\sqrt{1 - y^{2}}} d y$
$\Rightarrow x e^{x} - e^{x} = \sqrt{1 - y^{2}} + c$
$y (1) = - 1$
$\Rightarrow 0 = 0 + c \Rightarrow c = 0$
$∴ x e^{x} - e^{x} = \sqrt{1 - y^{2}}$
for $y (3)$ put $x = 3$
$3 e^{3} - e^{3} = \sqrt{1 - y^{2}}$
$\Rightarrow 4 e^{6} = 1 - y^{2}$
$\Rightarrow (y (3))^{2} = 1 - 4 e^{6}$

Suggest Corrections

Similar questions

Q. Let

y = y (x)

be a solution of the differential equation,

\sqrt{1 - x^{2}} \frac{d y}{d x} + \sqrt{1 - y^{2}} = 0, | x | < 1

.
If

y (\frac{1}{2}) = \frac{\sqrt{3}}{2}

, then

y (\frac{- 1}{\sqrt{2}})

is equal to:

Q. Let

y

be the solution of the differential equation

x \frac{d y}{d x} = \frac{y^{2}}{1 - y log x}

satisfying

y (1) = 1

. Then

y

satisfies

Q. If

y = y (x)

is the solution of the differential equation,

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

satisfying

y (1) = 1

, then

y (\frac{1}{2})

is equal to

Q. If

y = y (x)

is the solution of the differential equation,

e^{y} (\frac{d y}{d x} - 1) = e^{x}

such that

y (0) = 0

, then

y (1)

is equal to

Q. If for

x \geq 0

y = y (x)

is the solution of the differential equation

(1 + x) d y = [(1 + x)^{2} + y - 3] d x, y (2) = 0,

then y(3) is equal to

Join BYJU'S Learning Program

Let y=y(x) be the solution of the differential equation ex√1−y2 dx+(yx)dy=0, y(1)=−1. Then the value of (y(3))2 is equal to

The correct option is B 1−4e6 ex√1−y2dx=−yxdy ⇒∫xexdx=∫−y√1−y2dy ⇒xex−ex=√1−y2+c y(1)=−1 ⇒0=0+c⇒c=0 ∴xex−ex=√1−y2 for y(3) put x=3 3e3−e3=√1−y2 ⇒4e6=1−y2 ⇒(y(3))2=1−4e6

Let $y = y (x)$ be the solution of the differential equation $e^{x} \sqrt{1 - y^{2}} d x + (\frac{y}{x}) d y = 0,$ $y (1) = - 1.$ Then the value of $(y (3))^{2}$ is equal to