Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa

Let y=y(x) be a solution of the differential equation, \sqrt{1-x^{2}}\frac{dy}{dx}+\sqrt{1-y^{2}}=0,\left | x \right |<1. If y\left ( \frac{1}{2} \right )=\frac{\sqrt{3}}{2}, then y\left ( \frac{-1}{\sqrt{2}} \right ) is equal to :
Option: 1 -\frac{1}{\sqrt{2}}
Option: 2 -\frac{\sqrt{3}}{2}
Option: 3 \frac{1}{\sqrt{2}}
Option: 4 \frac{\sqrt{3}}{2}
 

Answers (1)

best_answer

 

 

Formation of Differential Equation and Solutions of a Differential Equation -

This is the general solution of the differential equation (2), which represents the family of the parabola (when a = 1) and one member of the family of parabola is given in Eq (1).

Also, Eq (1) is a particular solution of the differential equation (2).

 

The solution of the differential equation is a relation between the variables of the equation not containing the derivatives, but satisfying the given differential equation.

 

A general solution of a differential equation is a relation between the variables (not involving the derivatives) which contains the same number of the arbitrary constants as the order of the differential equation. 

 

Particular solution of the differential equation obtained from the general solution by assigning particular values to the arbitrary constant in the general solution.

-

 

 

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

{\frac{d y}{\sqrt{1-y^{2}}}=-\frac{d x}{\sqrt{1-x^{2}}} \Rightarrow \sin ^{-1} y=-\sin ^{-1} x+c} \\ {x=\frac{1}{2}, y=\frac{\sqrt{3}}{2} \Rightarrow \frac{\pi}{2}=-\frac{\pi}{6}-c}

\begin{aligned} \sin ^{-1} y &=\frac{\pi}{2}-\sin ^{-1} x \\ &=\cos ^{-1} x \Rightarrow y=\sin (\cos^{-1}x) \end{aligned}

y\left ( \frac{1}{\sqrt{2}} \right ) =\frac{1}{\sqrt2}

Correct Option (3)

Posted by

Kuldeep Maurya

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

JEE Main 2024 session 2 final answer key soon at jeemain.nta.ac.in; result on April 25
anam-khan

JEE Main 2024 Session 2: Last day to challenge answer key today
anam-khan

BTech admission 2024 without JEE; top government engineering colleges, upcoming entrance exams

Latest Question