Formation of Differential Equations

Form the differential equation of all line which makes intercept $3$ on $X-$axis.

Form the differential equation of $y=c{\left(x-c\right)}^2$, where, $c$ is an arbitrary constant.

The differential equation of family of circles $x^2+y^2+2\lambda x+c=0$, where $\lambda ,c$ both are parameters

Form the differential equation having $y={\left({\sin }^{-1}x\right)}^2+A{\cos }^{-1}x+B$ where $A$ and $B$ are arbitrary constants.

Form differential equation of locus of a point whose distance from origin is equal to distance from line $x+y+\lambda =0$ where $\lambda$ is a variable parameter.

Form differential equation of all straight lines at a distance unity from $\left(2,0\right)$.

Form differential equation of all circles touching both positive co-ordinate axes.

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

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

Form the differential equation of all parabolas whose axis is $Y-$axis.

Form the differential equation of all parabolas having the vertex at origin and axis along the positive $Y-$axis.

Form the differential equation of the family of circles touching the $X-$axis at the origin.

Find the differential equation of the family of circles having their centres on the line $y=10$ and touching the$X-$axis.

A particle is moving along the $X-$axis. Its acceleration at time $t$ is proportional to its velocity at that time. Find the differential equation of the motion of the particle.

Obtain the differential equation by eliminating the arbitrary constants from the following equation.

$y^2={\left(x+c\right)}^3$

Obtain the differential equation by eliminating the arbitrary constants from the following equation.

$y=\left(c_1+c_{2}x\right)e^x$

Obtain the differential equation by eliminating the arbitrary constants from the following equation.

$y=A \cos \left(\log x\right)+B\sin \left(\log x\right)$

Obtain the differential equation by eliminating the arbitrary constants: $y=c^2+\frac{c}{x}$