Suppose $y$ is a function of $x$ that satisfies $\frac{d y}{d x}=\frac{\sqrt{1-y^2}}{x^2}$ and $y=0$ at $x=\frac{2}{\pi}$, then $y\left(\frac{3}{\pi}\right)$ is equal to:

JEE MATHEMATICS MCQ: DIFFERENTIAL EQUATIONS

1 Easy

1 of 1

Application +4 | -1

Suppose

y

is a function of

x

that satisfies

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

and

y=0

x=\frac{2}{\pi}

, then

y\left(\frac{3}{\pi}\right)

is equal to:

View answer and explanation

Correct option: B

\frac{1}{2}

Option B (

\frac{1}{2}

) is correct because it's found by solving the differential equation and using the given initial condition to find the constant of integration.

Practice All Chapter MCQs →

y=y(x)

\left(3 y^{2}-5 x^{2}\right) y d x+2 x\left(x^{2}-y^{2}\right) d y=0

y(1)=1

\left|(y(2))^{3}-12 y(2)\right|

x

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

\left( {y' = \frac{{dy}}{{dx}},y'' = \frac{{{d^2}y}}{{d{x^2}}}} \right)

x = A\cos 4t + B\sin 4t,

\frac{{{d^2}x}}{{d{t^2}}}

y=y_{1}(x)

y=y_{2}(x)

\frac{d y}{d x}=y+7

y_{1}(0)=0

y_{2}(0)=1

y=y_{1}(x)

y=y_{2}(x)

y=y(t)

\frac{d y}{d t}+\alpha y=\gamma e^{-\beta t}

\alpha>0, \beta>0

\gamma>0

\lim \limits_{{x \rightarrow \infty}} y(t)