Basics of Differential Equation

If $f\left(x\right)f^{\text{'}}\left(-x\right)=f\left(-x\right)f^{\text{'}}\left(x\right)$, then the value of $f\left(x\right)f\left(-x\right)$ for all $x$ is given $f\left(0\right)=3$

Define differential equation. Find the order and degree of the following O.D.E ${\left(y^{\text{'}\text{'}\text{'}}\right)}^4+{\left(y^{\text{'}}\right)}^5=\sin x$.

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

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

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

Determine the order and degree of the following differential equation.

Determine the order and degree of the following differential equation.

$e^{\frac{dy}{dx}}+\frac{dy}{dx}=x$

Determine the order and degree of the following differential equation.

${\left(\frac{d^{3}y}{d{x}^3}\right)}^{\frac{1}{6}}.{\left(\frac{dy}{dx}\right)}^{\frac{1}{3}}=5$

Determine the order and degree of the following differential equation.

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

Determine the order and degree of the following differential equation.

$\frac{d^{4}y}{d{x}^4}={\left[1+{\left(\frac{dy}{dx}\right)}^2\right]}^3$

Determine the order and degree of the following differential equation.

$\frac{d^{2}x}{d{t}^2}+{\left(\frac{dx}{dt}\right)}^2+7=0$

Determine the order and degree of the following differential equation.

${\left(\frac{d^{2}y}{d{x}^2}\right)}^2+{\left(\frac{dy}{dx}\right)}^3=e^x$

If $m$ and $n$ are respectively the order and degree of the differential equation of the family of parabolas with focus at the origin and $X$-axis as its axis, then $mn-m+n=$

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

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

Find the degree of the differential equation $y_3^{2/3}+2+3y_2+y_1=0$

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