Basics of Differential Equation

Suppose $E$ is the differential equation representing family of curves $y^2=2cx+2c\sqrt{c}$ where $c$ is a positive parameter.

What is the degree of the differential equation?

Suppose $E$ is the differential equation representing family of curves $y^2=2cx+2c\sqrt{c}$ where $c$ is a positive parameter.

What is the order of the differential equation?

Find the order and degree of the differential equation ${\left(\frac{d^{3}y}{d{x}^3}\right)}^{\frac{2}{3}}-3\left(\frac{d^{2}y}{d{x}^2}\right)=5\left(\frac{dy}{dx}\right)$.

Find the order and degree of the differential equation ${\left(\frac{d^{3}y}{d{x}^3}\right)}^{2/3}-3\frac{d^{2}y}{d{x}^2}=5\frac{dy}{dx}$.

Degree of the differential equation $\frac{d^{2}y}{d{x}^2}+x^2\left(\frac{dy}{dx}\right)=e^x$ is:

Find the order and degree, if defined, of each of the following differential equation:

$y^{\text{'}\text{'}\text{'}}+y^2+e^{y^{\text{'}}}=0$ 

Find the order and degree, if defined, of each of the following differential equation:

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

Which of the following differential equation has an order of $2$ and a degree of $3$?

Find the order and degree of ${\left(y^{\text{'}\text{'}\text{'}}\right)}^3+y^{\text{'}\text{'}}+y^{\text{'}}+e^{y^{\text{'}}}=0$

Find the order and degree of ${\left[\frac{d^{3y}}{d{x}^3}\right]}^2-3{\left(\frac{dy}{dx}\right)}^2-e^x=4$

The sum of the degree and order of the differential equation ${\left(1+y_1^2\right)}^{\frac{2}{3}}=y_2$ is

For the differential equation $\sqrt{\frac{d^{2}y}{d{x}^2}}=\sqrt[3]{{\left[y\frac{dy}{dx}+x\sin \left(\frac{dy}{dx}\right)\right]}^2}$

The degree of the differential equation $x{\left(\frac{d^{2}y}{d{x}^2}\right)}^{\frac{1}{3}}+2x^2{\left(\frac{d^{2}y}{d{x}^2}\right)}^{\frac{5}{3}}+7\frac{dy}{dx}+y=0$

What is the order of the differential equation $\frac{dx}{dy}+\int ydx=x^3$?

Find the order and degree, if defined, of each of the following differential equation:

 $\frac{dy}{dx}-\cos x=0$

The order and degree of differential equation ${\left\{1+{\left(\frac{dy}{dx}\right)}^2\right\}}^{\frac{3}{2}}=\frac{d^{2}y}{d{x}^2}$ are $p$ and $q$ respectively then $p+q=\_\_\_\_\_$.

Order and degree of the differential equation $e^{\frac{d^{2}y}{d{x}^2}}=x$ are respectively.

Determine the order and degree (if exists) of the following differential equation:

$\frac{dy}{dx}=x+y+5$.

Let $y=f\left(x\right)$ is a curve such that slope of tangent at any point is equal to sum of ratio of ordinate and abscissa of that point and square of its abscissa. If the curve passes through $\left(1,-2\right)$, then $2{\int }_0^{1}f\left(x\right)dx$ is $\lambda$. Find $\left|\lambda \right|$

Write the sum of the order and the degree of the following differential equation:

$\frac{d}{dx}\left(\frac{dy}{dx}\right)=5$