Formation of Differential Equation

The order and the degree of the differential equation of all ellipses with centre at the origin, major axis along $X$-axis and eccentricity $\frac{\sqrt{3}}{2}$ are, respectively

The differential equation satisfied by the family of curves given by $y=ax\cos \left(\frac{1}{x}+b\right)$ is...

$($where $a, b$ are arbitrary constant$)$

The differential equation of all parabolas each of which has a latus rectum 4a and whose axes are parallel to the Y-axis is

The differential equation of all straight lines passing through the origin is

Differential equation of all family of lines $y=mx+\frac{4}{m}$ by eliminating the arbitrary constant $m$ is

The family of curves $y=e^{a\sin x}$, where $a$ is an arbitrary constant, is represented by the differential equation

Differential equation of family of ellipse whose centre is $\left(1,0\right)$ and major axis is $x$-axis is

Form the differential equation representing the family of curves $y=a \sin (x+b)$, where $a,b$ are arbitrary constant.

The differential equation by eliminating the arbitrary constants from the following equation: $y=c_1{e}^{2x}+c_2{e}^{-2x}$ will be

If $y={\left({\tan }^{-1}x\right)}^2$, then ${\left(x^2+1\right)}^2{y}_2+2x\left(x^2+1\right)y_1$ is equal to

The differential equation of the family of curves $y=a{e}^{3x}+b{e}^{-2x}$ by eliminating arbitrary constants $a$ and $b$ will be

The differential equation of the family of curves represented by $c(y+c{)}^2=x^3$ is

The differential equation satisfied by the curves $e^{2y}+2bx{e}^y+b^2=0$, where $b$ is a parameter, is

Find the order and degree of the differential equation of all tangent lines to the parabola given by, $2y=x^2$.

If $x^2+y^2=t+\frac{1}{t}, x^4+y^4=t^2+\frac{1}{t^2}$. If we eliminate parameter $t$ then the required differential equation will be

The differential equation satisfied by the family of curves given by $y=ax\cos \left(\frac{1}{x}+b\right)$ is

$($where $a, b$ are arbitrary constant$)$

What was the primary role of women in the Mughal agrarian economy?

The differential equation of the family of curves $p{y}^2=3x-p$ is (where $p$ is an arbitrary constant) is

The differential equation of the family of curves whose tangent at any point makes an angle of $\frac{\pi }{4}$ with the ellipse $\frac{x^2}{4}+y^2=1$ is

The differential equation of the family of circles with radius $5$ units and center on the line $y=2$ is