What is a differential equation and the order and degree of a differential equation?

What is differential equation and order and degree of a differential equation

Find the order and degree of the differential equation log_e(1+(d^2y)/dx^2)=x

Find the order and degree of the differential equation (dy)/(dx)+sin((dy)/(dx))=0

Find the order and degree of the following differential equations. (dy)/(dx)+y=logx

From the differential equation of the family of parabolas with focus at the origin and axis of symmetry along the x-axis. Find the order and degree of the differential equation.

If a and b are arbitrary constants, then the order and degree of the differential equation of the family of curves ax^(2)+by^(2)=2 respectively are

STATEMENT-1 : If m and n are respectively order and degree of differential equation , then m and n are mutually independent. STATEMENT-2 : If general solution of a differential equation contains two arbitrary constants, then its order is 2. STATEMENT-3 : The order and degree of differential equation sqrt(1+((dy)/(dx))^(2)) = (x(d^(2)y)/(dx^(2)))^(1//3) are 2 and 2 respectively.

If m and n are the order and degree of the differential equation (y'')^(5)+4 . ((y'')^(3))/(y''')+y'''=sin x, then

Statement 1 : Order of a differential equation represents the number of arbitrary constants in the general solution. Statement 2 : Degree of a differential equation represents the number of family of curves. Which of the following Statement is/are are correct ?

Write the sum of the order and degree of the differential equation : d/(dx){((dy)/(dx))^4}=0