$y = mx + \frac{2}{m}$ is the general solution of
- A$y\left(\frac{dy}{dx}\right)^{2} = x\left(\frac{dy}{dx}\right) + 2$
- B$y = x \frac{dy}{dx} + 2$
- C$y\left(\frac{dy}{dx}\right) = x\left(\frac{dy}{dx}\right)^{2} + 2$
- D$y\left(\frac{dy}{dx}\right) = x + 2$
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Form the differential equation of the family of circles in the first quadrant which touch the coordinate axes.
Difficult
View SolutionThe differential equation for which $l x^2+m y^2=x+y$ is the general solution is
Statement $I$: The differential equation corresponding to the family of circles having their centres on $Y$-axis and fixed radius $k$ is $(x^2-k^2)(\frac{dy}{dx})^2+x^2=0$.
Statement $II$: The differential equation corresponding to the family of circles passing through the origin and having their centres on $X$-axis is $x^2-y^2+2xy \frac{dy}{dx}=0$.
Which of the above statements is (are) true?
Statement $II$: The differential equation corresponding to the family of circles passing through the origin and having their centres on $X$-axis is $x^2-y^2+2xy \frac{dy}{dx}=0$.
Which of the above statements is (are) true?
The differential equation of all parabolas whose axis is the $y$-axis is:
DifficultMHT CET 2021
View SolutionThe differential equation of all parabolas whose axes are parallel to the $Y$-axis is:
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