English

Determine the order and degree of the following differential equations. dydx=7d2ydx2

Advertisements
Advertisements

Question

Determine the order and degree of the following differential equations.

`dy/dx = 7 (d^2y)/dx^2`

Sum
Advertisements

Solution

`dy/dx = 7 (d^2y)/dx^2`

By definition of order and degree,

Order : 2 ; Degree : 1

shaalaa.com
  Is there an error in this question or solution?
Chapter 8: Differential Equation and Applications - Exercise 8.1 [Page 162]

APPEARS IN

Balbharati Mathematics and Statistics 1 (Commerce) [English] Standard 12 Maharashtra State Board
Chapter 8 Differential Equation and Applications
Exercise 8.1 | Q 1.6 | Page 162

RELATED QUESTIONS

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

y' + 5y = 0


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

y′′′ + 2y″ + y′ = 0


\[2\frac{d^2 y}{d x^2} + 3\sqrt{1 - \left( \frac{dy}{dx} \right)^2 - y} = 0\]

\[y = x\frac{dy}{dx} + a\sqrt{1 + \left( \frac{dy}{dx} \right)^2}\]

\[y = px + \sqrt{a^2 p^2 + b^2},\text{ where p} = \frac{dy}{dx}\]

\[\left( \frac{dy}{dx} \right)^3 - 4 \left( \frac{dy}{dx} \right)^2 + 7y = \sin x\]

Write the order of the differential equation of the family of circles touching X-axis at the origin.


Write the order and degree of the differential equation
\[\frac{d^2 y}{d x^2} + \left( \frac{dy}{dx} \right)^\frac{1}{4} + x^\frac{1}{5} = 0\]


The order of the differential equation \[2 x^2 \frac{d^2 y}{d x^2} - 3\frac{dy}{dx} + y = 0\], is


Choose the correct option from the given alternatives:

The order and degree of the differential equation `sqrt(1 + ("dy"/"dx")^2) = (("d"^2"y")/"dx"^2)^(3/2)` are respectively.


Determine the order and degree of the following differential equation:

`("d"^2"y")/"dx"^2 + 5 "dy"/"dx" + "y" = "x"^3`


Determine the order and degree of the following differential equations.

`(d^4y)/dx^4 + [1+(dy/dx)^2]^3 = 0`


Find the order and degree of the following differential equation:

`[ (d^3y)/dx^3 + x]^(3/2) = (d^2y)/dx^2`


Find the order and degree of the following differential equation:

`x+ dy/dx = 1 + (dy/dx)^2`


The order and degree of `((dy)/(dx))^3 - (d^3y)/(dx^3) + ye^x` = 0 are ______.


Choose the correct alternative:

The order and degree of `(1 + (("d"y)/("d"x))^3)^(2/3) = 8 ("d"^3y)/("d"x^3)` are respectively


Order and degree of differential equation are always ______ integers


State whether the following statement is True or False: 

Order and degree of differential equation are always positive integers.


 Order of highest derivative occurring in the differential equation is called the degree of the differential equation


The order of the differential equation of all circles whose radius is 4, is ______.


The order of the differential equation whose general solution is given by `y=C_(1)e^(2x+C_2)+C_3e^x+C_4sin(x+C_5)` is ______.


The order of the differential equation of all circles of radius r, having centre on X-axis and passing through the origin is ______.


The degree of the differential equation `(1 + "dy"/"dx")^3 = (("d"^2y)/("d"x^2))^2` is ______.


Order of the differential equation representing the family of ellipses having centre at origin and foci on x-axis is two.


Degree of the differential equation `sqrt(1 + ("d"^2y)/("d"x^2)) = x + "dy"/"dx"` is not defined.


Polio drops are delivered to 50 K children in a district. The rate at which polio drops are given is directly proportional to the number of children who have not been administered the drops. By the end of 2nd week half the children have been given the polio drops. How many will have been given the drops by the end of 3rd week can be estimated using the solution to the differential equation `"dy"/"dx" = "k"(50 - "y")` where x denotes the number of weeks and y the number of children who have been given the drops.

State the order of the above given differential equation.


The order and degree of the differential equation `sqrt(dy/dx) - 4 dy/dx - 7x` = 0 are ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×