Day 396: MHT-CET Maths

1. A.
   $\ x\frac{\text{ }dy}{\text{ }dx} + xy = 0$
2. B.
   $\ x^{2}\frac{\text{ }dy}{\text{ }dx} + 2xy - 4e^{x} = 0$
3. C.
   $\ x\frac{\text{ }dy}{\text{ }dx} + (x - 2)y = 0$
4. D.
   $x\frac{\text{ }dy}{\text{ }dx} + (2 - x)y = 0$

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1. A.
   0
2. B.
   1
3. C.
   $-3$
4. D.
   3

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1. A.
   $y = \cos x + \frac{2\sin x}{x} + \frac{2}{x^{2}}\cos x + \frac{x}{3}\log x - \frac{x}{9} + \frac{c}{x^{2}}$, where c is the constant of integration.
2. B.
   $\ y = - \cos x - \frac{2}{x}\sin x + \frac{2}{x^{2}}\cos x + \frac{x}{3}\log x - \frac{x}{9} + \frac{c}{x^{2}}$ where c is the constant of integration.
3. C.
   $y = - \cos x + \frac{2}{x}\sin x + \frac{2}{x^{2}}\cos x + \frac{x}{3}\log x - \frac{x}{9} + \frac{c}{x^{2}},$where $c$ is the constant of integration.
4. D.
   $y = \cos x - \frac{2}{x}\sin x + \frac{2}{x^{3}}\cos x + \frac{x}{3}\log x - \frac{x}{9} + \frac{c}{x^{2}}$ where c is the constant of intergration.

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1. A.
   0.2762
2. B.
   0.1852
3. C.
   0.2074
4. D.
   0.7235

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1. A.
   $\frac{4\sqrt{2}}{\log7 \cdot \log9}$
2. B.
   $4\sqrt{2}\log7 \cdot \log9$
3. C.
   $4\sqrt{2}\log63$
4. D.
   $\frac{\log7 \cdot \log9}{4\sqrt{2}}$

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