MHT CET 2025 22nd April Morning Shift | Differential Equations Question 22 | Mathematics

The degree of the differential equation $\frac{\mathrm{d}^2 y}{\mathrm{~d} x^2}+3\left(\frac{\mathrm{~d} y}{\mathrm{~d} x}\right)^2=x^2 \log \left(\frac{\mathrm{~d}^2 y}{\mathrm{~d} x^2}\right)$ is

Not defined

MHT CET 2025 22nd April Morning Shift

MCQ (Single Correct Answer)

-0

If $y+\frac{\mathrm{d}}{\mathrm{d} x}(x y)=x(\sin x+\log x)$ then

$y=\cos x+\frac{2 \sin x}{x}+\frac{2}{x^2} \cos x+\frac{x}{3} \log x-\frac{x}{9}+\frac{\mathrm{c}}{x^2}$, where c is the constant of integration.

$y=-\cos x-\frac{2}{x} \sin x+\frac{2}{x^2} \cos x+\frac{x}{3} \log x-\frac{x}{9}+\frac{\mathrm{c}}{x^2}$ where c is the constant of integration.

$$ \begin{aligned} y=-\cos x+\frac{2}{x} \sin x+ & \frac{2}{x^2} \cos x +\frac{x}{3} \log x-\frac{x}{9}+\frac{c}{x^2}\text { where } \mathrm{c} \text { is the constant of integration. }\end{aligned} $$

$y=\cos x-\frac{2}{x} \sin x+\frac{2}{x^3} \cos x+\frac{x}{3} \log x-\frac{x}{9}+\frac{\mathrm{c}}{x^2}$ where $c$ is the constant of intergration.

MHT CET 2025 22nd April Morning Shift

MCQ (Single Correct Answer)

-0

The population of a town increases at a rate proportional to the population at that time. If the population increases from forty thousand to eighty thousand in 20 years, then the population in another 40 years will be

240000

160000

320000

640000

MHT CET 2025 21st April Evening Shift

MCQ (Single Correct Answer)

-0

A particular solution of $3 \mathrm{e}^x \tan y \mathrm{~d} x+\left(1-\mathrm{e}^x\right) \sec ^2 y \mathrm{~d} y=0$ with $y(1)=\frac{\pi}{4}$ is

$\quad \tan y=\left(\frac{1-\mathrm{e}^3}{1-\mathrm{e}^x}\right)^3$

$\quad \tan y=\left(\frac{1-\mathrm{e}^2}{1-\mathrm{e}^x}\right)^3$

$\quad \tan y=\left(\frac{1-\mathrm{e}}{1-\mathrm{e}^x}\right)^3$

$\quad \tan y=\left(\frac{1-\mathrm{e}^x}{1-\mathrm{e}}\right)^3$

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