WB JEE 2008 | Differential Equations Question 2 | Mathematics

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WB JEE 2008

MCQ (Single Correct Answer)

-0.25

The differential equation of all parabolas whose axes are parallel to y-axis is

$${{{d^3}y} \over {d{x^3}}} = 0$$

$${{{d^2}y} \over {d{x^2}}} = 0$$

$${{{d^2}y} \over {d{x^2}}} + {{dy} \over {dx}} = 0$$

$${{{d^2}y} \over {d{x^2}}} + {{dy} \over {dx}} + y = 0$$

WB JEE 2008

MCQ (Single Correct Answer)

-0.25

The solution of the differential equation $${{dy} \over {dx}} = {e^{y + x}} + {e^{y - x}}$$ is

$${e^{ - y}} = {e^x} - {e^{ - x}} + c,\,c$$ integrating constant

$${e^{ - y}} = {e^{ - x}} - {e^x} + c,\,c$$ integrating constant

$${e^{ - y}} = {e^x} + {e^{ - x}} + c,\,c$$ integrating constant

$${e^{ - y}} + {e^x} + {e^{ - x}} = c,\,c$$ integrating constant

WB JEE 2008

MCQ (Single Correct Answer)

-0.25

The order and degree of the following differential equation $${\left[ {1 + {{\left( {{{dy} \over {dx}}} \right)}^2}} \right]^{5/2}} = {{{d^3}y} \over {d{x^3}}}$$ are respectively

3, 2

3, 10

2, 3

3, 5

WB JEE 2008

MCQ (Single Correct Answer)

-0.25

The differential equation of the family of circles passing through the fixed points (a, 0) and ($$-$$a, 0) is

y₁(y² $$-$$ x²) + 2xy + a² = 0

y₁y² + xy + a²x² = 0

y₁(y² $$-$$ x² + a²) + 2xy = 0

y₁(y² + x²) $$-$$ 2xy + a² = 0

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