English

Determine the Order and Degree (If Defined) of the Following Differential Equation:- (Y"')2 + (Y")3 + (Y')4 + Y5 = 0 - Mathematics

Advertisements
Advertisements

Question

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

(y"')2 + (y")3 + (y')4 + y5 = 0

Short/Brief Note
Sum
Advertisements

Solution

(y"')2 + (y")3 + (y')4 + y5 = 0

The highest order derivative in the given equation is y''' and its power is 2.

Therefore, the given differential equation is of third order and second degree.

i.e., Order = 3 and degree = 2

shaalaa.com
  Is there an error in this question or solution?
Chapter 22: Differential Equations - Revision Exercise [Page 144]

APPEARS IN

RD Sharma Mathematics [English] Class 12
Chapter 22 Differential Equations
Revision Exercise | Q 1.3 | Page 144

RELATED QUESTIONS

Order and degree of the differential equation `[1+(dy/dx)^3]^(7/3)=7(d^2y)/(dx^2)` are respectively 

(A) 2, 3

(B) 3, 2

(C) 7, 2

(D) 3, 7


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

`(d^2y)/(dx^2)^2 + cos(dy/dx) = 0`


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

( y′′′) + (y″)3 + (y′)4 + y5 = 0


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

y″ + 2y′ + sin y = 0


For the differential equation given below, indicate its order and degree (if defined).

`(d^2y)/dx^2 + 5x(dy/dx)^2 - 6y = log x`


\[\left( \frac{d^2 y}{d x^2} \right)^2 + \left( \frac{dy}{dx} \right)^2 = x \sin \left( \frac{d^2 y}{d x^2} \right)\]

(y'')2 + (y')3 + sin y = 0


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


Write the degree of the differential equation \[\left( 1 + \frac{dy}{dx} \right)^3 = \left( \frac{d^2 y}{d x^2} \right)^2\]


Write the degree of the differential equation \[\frac{d^2 y}{d x^2} + 3 \left( \frac{dy}{dx} \right)^2 = x^2 \log\left( \frac{d^2 y}{d x^2} \right)\]


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


In the following verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation:-

y = x2 + 2x + C            y' − 2x − 2 = 0


Write the order and the degree of the following differential equation: `"x"^3 ((d^2"y")/(d"x"^2))^2 + "x" ((d"y")/(d"x"))^4 = 0`


Determine the order and degree of the following differential equation:

`(dy)/(dx) = (2sin x + 3)/(dy/dx)`


Determine the order and degree of the following differential equation:

`("d"^2"y")/"dx"^2 + "dy"/"dx" + "x" = sqrt(1 + ("d"^3"y")/"dx"^3)`


Determine the order and degree of the following differential equations.

`(d^2x)/(dt^2)+((dx)/(dt))^2 + 8=0`


Find the order and degree of the following differential equation:

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


Select and write the correct alternative from the given option for the question

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


Degree of the given differential equation

`(("d"^3"y")/"dx"^2)^2 = (1 + "dy"/"dx")^(1/3)` is


The order and degree of the differential equation `[1 + ["dy"/"dx"]^3]^(7/3) = 7 (("d"^2"y")/"dx"^2)` are respectively.


The order of the differential equation of all circles which lie in the first quadrant and touch both the axes is ______.


The differential equation of the family of curves y = ex (A cos x + B sin x). Where A and B are arbitary constants is ______.


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


The order of the differential equation of all circles of given radius a is ______.


The degree of the differential equation `("d"^2y)/("d"x^2) + (("d"y)/("d"x))^3 + 6y^5` = 0 is ______.


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


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

`d/(dx) (dy/dx)` = 5


The degree of the differential equation `dy/dx - x = (y - x dy/dx)^-4` is ______.


The degree and order of the differential equation `[1 + (dy/dx)^3]^(7/3) = 7((d^2y)/(dx^2))` respectively are ______.


The order and degree of the differential eqµation whose general solution is given by `(d^2y)/(dx^2) + (dy/dx)^50` = In `((d^2y)/dx^2)` respectively, are ______.


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


Find the order and degree of the differential equation

`sqrt(1 + 1/(dy/dx)^2) = ((d^2y)/(dx^2))^(3/2)`


Find the order and degree of the differential equation `(1 + 3 dy/dx)^(2/3) = 4((d^3y)/(dx^3))`.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×