WB JEE 2011 | Differential Equations Question 29 | Mathematics

WB JEE 2011

MCQ (Single Correct Answer)

-0.25

Integrating factor (I.F.) of the differential equation $${{dy} \over {dx}} - {{3{x^2}} \over {1 + {x^3}}}y = {{{{\sin }^2}x} \over {1 + x}}$$ is

$${e^{1 + {x^3}}}$$

$$\log (1 + {x^3})$$

$$1 + {x^3}$$

$${1 \over {1 + {x^3}}}$$

WB JEE 2011

MCQ (Single Correct Answer)

-0.25

The differential equation of y = ae^bx (a & b are parameters) is

$$y{y_1} = y_2^2$$

$$y{y_2} = y_1^2$$

$$yy_1^2 = {y_2}$$

$$yy_2^2 = {y_1}$$

WB JEE 2012

MCQ (Single Correct Answer)

-0.33

The general solution of the differential equation $${{dy} \over {dx}} = {{x + y + 1} \over {2x + 2y + 1}}$$ is

$${\log _e}|3x + 3y + 2| + 3x + 6y = C$$

$${\log _e}|3x + 3y + 2| - 3x + 6y = C$$

$${\log _e}|3x + 3y + 2| - 3x - 6y = C$$

$${\log _e}|3x + 3y + 2| + 3x - 6y = C$$

WB JEE 2026

MCQ (Single Correct Answer)

-0.25

The solution of the differential equation $2 x^2 y \frac{d y}{d x}=\tan \left(x^2 y^2\right)-2 x y^2$, given $y(1)=\sqrt{\frac{\pi}{2}}$ is

$\quad \sin \left(x^2 y^2\right)=e^{x-1}$

$\quad \sin \left(x^2 y^2\right)=e^{2(x-1)}$

$\quad \cos \left(\frac{\pi}{2}+x^2 y^2\right)+x=0$

$\sin \left(x^2 y^2\right)=1$

WB JEE Subjects

Browse all chapters by subject