A continuously differential function $\phi \left( x \right)$ in $\left( {0,\pi } \right)$ satisfying $y' = 1 + {y^2},y\left( 0 \right) = 0 = y\left( \pi \right)$, is

$\left( {x - \pi } \right)\left( {1 - {e^x}} \right)$

JEE MATHEMATICS MCQ: DIFFERENTIAL EQUATIONS

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Analyzing +4 | -1

A continuously differential function

\phi \left( x \right)

\left( {0,\pi } \right)

satisfying

y' = 1 + {y^2},y\left( 0 \right) = 0 = y\left( \pi \right)

, is

View answer and explanation

Correct option: D

Not possible

Option D (Not possible) is correct because the solution to the differential equation is not continuous in the given interval.

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)