Basics of Differential Equations

Find the singular solution of the differential equation $y=x\frac{dy}{dx}-{\left(\frac{dy}{dx}\right)}^3$.

Find the singular solution for differential equation $y=x\frac{dy}{dx}+{\left(\frac{dy}{dx}\right)}^2+2$.

Find the singular solution of $y=x\frac{dy}{dx}+{\left(\frac{dy}{dx}\right)}^2+\frac{dy}{dx}$.

Find the singular solution of $y=x\frac{dy}{dx}+{\left(\frac{dy}{dx}\right)}^2$.

A differential equation is considered to be partial differential equation if it has

The degree of a differential equation whose general solution is given by $y=A\sin x+B\cos x+C$ where $A,B,C$ are arbitrary constants, is

${\left(dy\right)}^2+dy+y^2=y$ is an ordinary differential equation.

Which of the following is/are an ordinary differential equation/s?

The differential equation whose general solution is $y=\log x+c$ is

The general solution of the differential equation $\frac{dy}{dx}=\frac{2y}{x}$ is,

Order and degree of differential equation $\frac{d^{4}y}{ d{x}^4}={\left[1+{\left(\frac{dy}{ dx}\right)}^2\right]}^3$ respectively are

The order of the differential equation obtained by eliminating arbitrary constants in the family of curves $c_{1}y=\left(c_2+c_3\right)e^{x+c_4}$ is

Find the sum of the order and degree of the differential equation $y=x{\left(\frac{dy}{dx}\right)}^3+\frac{d^{2}y}{d{x}^2}$.

Find the differential equation of all non-vertical lines in a plane.

The order and degree of the differential equation $\frac{d^{4}y}{d{x}^4}-4\frac{d^{3}y}{d{x}^3}+8\frac{d^{2}y}{d{x}^2}-8\frac{dy}{dx}+4y=0$ are respectively.

$\frac{d^{3}y}{d{x}^3}+2\left(1+\frac{d^{2}y}{d{x}^2}\right)=1$ has degree and order respectively as

The order and degree of the differential equation ${\left(\frac{d^{2}y}{d{x}^2}\right)}^3+{\left(\frac{dy}{dx}\right)}^4-xy=0$ are respectively

The differential equation $x{\left(\frac{d^{2}y}{d{x}^2}\right)}^3+{\left(\frac{dy}{dx}\right)}^{4}y=x^2$ is of

The order and degree of the differential equation ${\left(\frac{d^{2}s}{d{t}^2}\right)}^2+3{\left(\frac{ds}{dt}\right)}^3+4=0$ are

The order and degree of the differential equation $5{\left(\frac{d^{2}y}{d{x}^2}\right)}^5+4{\left(\frac{d^{3}y}{d{x}^3}\right)}^2+{\left(\frac{dy}{dx}\right)}^3+2y+x^3=0$ are respectively