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

Determine the order and degree of the following differential equations. (d2ydx2)2+(dydx)2=ax - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

Determine the order and degree of the following differential equations.

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

बेरीज

उत्तर

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

By definition of order and degree,

Order : 2 ; 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] 12 Standard HSC Maharashtra State Board
पाठ 8 Differential Equation and Applications
Exercise 8.1 | Q 1.2 | पृष्ठ १६२

संबंधित प्रश्‍न

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

y″ + 2y′ + sin y = 0


\[s^2 \frac{d^2 t}{d s^2} + st\frac{dt}{ds} = s\]

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


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

y"' + 2y" + y' = 0


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

y" + 2y' + sin y = 0


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

y = cos x + C            y' + sin x = 0


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 equation:

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


Determine the order and degree of the following differential equations.

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


Fill in the blank:

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


Order and degree of a 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 and degree of the differential equation `(dy/dx)^3 + ((d^3y)/dx^3) + xy = 0` 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 of all circles of radius r, having centre on X-axis and passing through the origin 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 = ______.


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


The sum of the order and the degree of the differential equation `d/dx[(dy/dx)^3]` is ______.


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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×