WB JEE 2017 | Differential Equations Question 50 | Mathematics

WB JEE 2017

MCQ (Single Correct Answer)

-0.25

If $$y = {e^{m{{\sin }^{ - 1}}x}}$$ then $$(1 - {x^2}){{{d^2}y} \over {d{x^2}}} - x{{dy} \over {dx}} - $$ky = 0, where k is equal to

m²

$$-$$ 1

$$-$$ m²

WB JEE 2017

MCQ (Single Correct Answer)

-0.25

Solution of $${(x + y)^2}{{dy} \over {dx}} = {a^2}$$ ('a' belong a constant) is

$${{(x + y)} \over a} = \tan {{y + C} \over a},C$$ is an arbitrary constant

$$xy = a\tan Cx,C$$ is an arbitrary constant

$${x \over a} = \tan {y \over C},C$$ is an arbitrary constant

$$xy = \tan (x + C),C$$ is an arbitrary constant

WB JEE 2017

MCQ (Single Correct Answer)

-0.25

The integrating factor of the first order differential equation $${x^2}({x^2} - 1){{dy} \over {dx}} + x({x^2} + 1)y = {x^2} - 1$$ is

e^x

$$x - {1 \over x}$$

$$x + {1 \over x}$$

$${1 \over {{x^2}}}$$

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