MHT CET 2025 25th April Morning Shift | Differential Equations Question 6 | Mathematics

The rate at which the population of a city increases varies as the population. In a period of 20 years, the population increased from 4 lakhs to 6 lakhs. In another 20 years the population will be

8 lakhs

12 lakhs

9 lakhs

10 lakhs

MHT CET 2025 25th April Morning Shift

MCQ (Single Correct Answer)

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The differential equation $x \frac{\mathrm{~d} y}{\mathrm{~d} x}=2 y$ represents ________

a family of circles with radius c .

a family of parabolas with vertex at the origin and axis along the positive Y -axis

a family of parabolas with vertex at origin and axis along the positive X -axis

a family of ellipses

MHT CET 2025 25th April Morning Shift

MCQ (Single Correct Answer)

-0

The solution of the equation $x^2 y-x^3 \frac{\mathrm{~d} y}{\mathrm{~d} x}=y^4 \cos x$, where $y(0)=1$, is

$y^3=3 x^2 \sin x$

$x^3=3 y^3 \sin x$

$x^3=y^3 \sin x$

$y^3=4 x^3 \sin x$

MHT CET 2025 25th April Morning Shift

MCQ (Single Correct Answer)

-0

$y=\mathrm{e}^x(\mathrm{~A} \cos x+\mathrm{B} \sin x)$ is the solution of the differential equation

$x^2 \frac{\mathrm{~d}^2 y}{\mathrm{~d} x^2}+\left(1+y^2\right)=0$

$\frac{\mathrm{d}^2 y}{\mathrm{~d} x^2}-\frac{\mathrm{d} y}{\mathrm{~d} x}+y=0$

$\frac{\mathrm{d}^2 y}{\mathrm{~d} x^2}-2 \frac{\mathrm{~d} y}{\mathrm{~d} x}+2 y=0$

$x \frac{\mathrm{~d}^2 y}{\mathrm{~d} x^2}-2 \frac{\mathrm{~d} y}{\mathrm{~d} x}+2 y=0$

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