Let $ y=f(x) $ be the solution of the differential equation $ y(x+1) d x-x^{2} d y=0, y(1)=e $. Then $\mathop {\lim }\limits_{x \to 0} f(x)$ is equal to

JEE MATHEMATICS MCQ: DIFFERENTIAL EQUATIONS

1 Easy

1 of 1

Application +4 | -1

Let

y=f(x)

be the solution of the differential equation

y(x+1) d x-x^{2} d y=0, y(1)=e

. Then

\lim\limits_{x \to 0} f(x)

is equal to

View answer and explanation

Correct option: B

Option B (0) is correct because the limit of the function

f(x)

x

approaches 0 is 0, as derived from the solution of the differential equation.

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)