मराठी
महाराष्ट्र राज्य शिक्षण मंडळएचएससी वाणिज्य (इंग्रजी माध्यम) इयत्ता १२ वी

Determine the order and degree of the following differential equations. (y′′′)2+2(y′′)2+6y′+7y=0

Advertisements
Advertisements

प्रश्न

Determine the order and degree of the following differential equations.

`(y''')^2 + 2(y'')^2 + 6y' + 7y = 0`

बेरीज
Advertisements

उत्तर

`(y''')^2 + 2(y'')^2 + 6y' + 7y = 0`

By definition of order and degree,

Order : 3 ; Degree : 2

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 8: Differential Equation and Applications - Exercise 8.1 [पृष्ठ १६२]

APPEARS IN

बालभारती Mathematics and Statistics 1 (Commerce) [English] Standard 12 Maharashtra State Board
पाठ 8 Differential Equation and Applications
Exercise 8.1 | Q 1.4 | पृष्ठ १६२

संबंधित प्रश्‍न

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′′′ + 2y″ + y′ = 0


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

`(d^4y)/dx^4 - sin ((d^3y)/(dx^3)) = 0`


For the given below, verify that the given function (implicit or explicit) is a solution to the corresponding differential equation.

`y = e^x (acos x + b sin x)  :  (d^2y)/(dx^2) - 2 dy/dx + 2y = 0`


The degree of the differential equation \[\left( \frac{d^2 y}{d x^2} \right)^2 - \left( \frac{dy}{dx} \right) = y^3\], is


The degree of the differential equation \[\left( \frac{d^2 y}{d x^2} \right)^3 + \left( \frac{dy}{dx} \right)^2 + \sin\left( \frac{dy}{dx} \right) + 1 = 0\], is


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

\[\left( \frac{ds}{dt} \right)^4 + 3s\frac{d^2 s}{d t^2} = 0\]


Write the order and degree of the differential equation `((d^4"y")/(d"x"^4))^2 =  [ "x" + ((d"y")/(d"x"))^2]^3`.


Determine the order and degree of the following differential equation:

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


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"^3"y")/"dx"^3)^(1/2) - ("dy"/"dx")^(1/3) = 20`


Find the order and degree of the following differential equation:

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


Order and degree of differential equation are always ______ integers


State whether the following statement is True or False: 

The degree of a differential equation is the power of highest ordered derivative when all the derivatives are made free from negative and/or fractional indices if any


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


The order and degree of the differential equation `[1 + 1/("dy"/"dx")^2]^(5/3) = 5 ("d"^2y)/"dx"^2` are respectively.


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 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 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 parabolas y2 = 4ax is ______.


The order and degree of the differential equation `(("d"^3y)/("d"x^3))^2 - 3 ("d"^2y)/("d"x^2) + 2(("d"y)/("d"x))^4` = y4 are ______.


If m and n, respectively, are the order and the degree of the differential equation `d/(dx) [((dy)/(dx))]^4` = 0, then m + n = ______.


Find the general solution of the following differential equation:

`(dy)/(dx) = e^(x-y) + x^2e^-y`


The differential equation representing the family of curves y2 = `2c(x + sqrt(c))`, where c is a positive parameter, is of ______.


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


Find the order and degree of the differential equation

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


Assertion: Degree of the differential equation: `a(dy/dx)^2 + bdx/dy = c`, is 3

Reason: If each term involving derivatives of a differential equation is a polynomial (or can be expressed as polynomial) then highest exponent of the highest order derivative is called the degree of the differential equation.

Which of the following is correct?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×