JEE MATHEMATICS MCQ: DIFFERENTIAL EQUATIONS

1 Easy

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Application +4 | -1

The solution of the differential equation

\frac{d y}{d x}=\frac{1+y^2}{1+x^2}

, is

View answer and explanation

Correct option: B

d y-x=C(1+x y)

Option B (

dy - x = C(1 + xy)

) is correct because it is the result of separating variables, integrating, and using the tangent subtraction formula.

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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

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\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_{1}(0)=0

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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)