JEE MATHEMATICS MCQ: DIFFERENTIAL EQUATIONS

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The general solution of the differential equation

\frac{{dy}}{{dx}} = \frac{{\left( {1 + {y^2}} \right)}}{{xy\left( {1 + {x^2}} \right)}}

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Correct option: B

\left( {1 + {x^2}} \right)\left( {1 + {y^2}} \right) = c{x^2}

The correct answer is

\left( {1 + {x^2}} \right)\left( {1 + {y^2}} \right) = c{x^2}

because it is the result of separating variables and integrating the given differential equation.

More Questions from DIFFERENTIAL EQUATIONS

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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

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

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

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y=y_{2}(x)

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

y_{1}(0)=0

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y=y_{1}(x)

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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)