MHT CET 2021 21th September Evening Shift | Differential Equations Question 43 | Mathematics

If $$m$$ is order and $$n$$ is degree of the differential equation $$\left(\frac{d^2 y}{d x^2}\right)^5+4 \frac{\left(\frac{d^2 y}{d x^2}\right)}{\left(\frac{d^3 y}{d x^3}\right)}+\left(\frac{d^3 y}{d x^3}\right)=x^2$$ then

$$\mathrm{m}=3, \mathrm{n}=1$$

$$\mathrm{m}=3, \mathrm{n}=2$$

$$\mathrm{m}=3, \mathrm{n}=3$$

$$\mathrm{m}=3, \mathrm{n}=5$$

MHT CET 2021 21th September Morning Shift

MCQ (Single Correct Answer)

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The general solution of the differential equation $$\left(3 x y+y^2\right) d x+\left(x^2+x y\right) d y=0$$ is

$$x^2\left(2 x y-y^2\right)=c$$

$$x^2\left(y^2-2 x y\right)=c$$

$$x\left(2 x y+y^2\right)=c$$

$$x^2\left(2 x y+y^2\right)=c$$

MHT CET 2021 21th September Morning Shift

MCQ (Single Correct Answer)

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The differential equation of family of circles whose centres lie on $$\mathrm{X}$$-axis is

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

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

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

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

MHT CET 2021 21th September Morning Shift

MCQ (Single Correct Answer)

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The general solution of the differential equation $$y(1+\log x)\left(\frac{d x}{d y}\right)-x \log x=0$$ is

$$y(1+\log x)=c$$

$$x \log x=y c$$

$$x \log x=y+c$$

$$\log x-y=c$$

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