हिंदी

Determine the order and degree (if defined) of the differential equation: y′′′ + 2y″ + y′ = 0 - Mathematics

Advertisements
Advertisements

प्रश्न

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

y′′′ + 2y″ + y′ = 0

टिप्पणी लिखिए

उत्तर

y′′′ + 2y″ + y′ = 0

The highest-order derivative is y′′′, which has a degree of 2.

Thus, the provided differential equation has order 3 and degree 2.

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 9: Differential Equations - Exercise 9.1 [पृष्ठ ३८२]

APPEARS IN

एनसीईआरटी Mathematics [English] Class 12
अध्याय 9 Differential Equations
Exercise 9.1 | Q 7 | पृष्ठ ३८२

वीडियो ट्यूटोरियलVIEW ALL [3]

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:

`(d^2y)/(dx^2)` = cos 3x + sin 3x


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

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


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

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


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


The degree of the differential equation \[\frac{d^2 y}{d x^2} + e^\frac{dy}{dx} = 0\]


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 \[\left\{ 5 + \left( \frac{dy}{dx} \right)^2 \right\}^{5/3} = x^5 \left( \frac{d^2 y}{d x^2} \right)\], is


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

y" + (y')2 + 2y = 0


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

y"' + y2 + ey' = 0


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

y = x sin x              `xy'=y+xsqrt(x^2-y^2)`


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 equation:

`("d"^4"y")/"dx"^4 + sin ("dy"/"dx") = 0`


Determine the order and degree of the following differential equation:

`(("d"^3"y")/"dx"^3)^2 = root(5)(1 + "dy"/"dx")`


Determine the order and degree of the following differential equations.

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


Determine the order and degree of the following differential equations.

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


Fill in the blank:

Order and degree of a differential equation are always __________ integers.


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`


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


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


The degree of the differential equation `("d"^4"y")/"dx"^4 + sqrt(1 + ("dy"/"dx")^4)` = 0 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 and degree of the differential equation `[1 + 1/("dy"/"dx")^2]^(5/3) = 5 ("d"^2y)/"dx"^2` are respectively.


The differential equation `x((d^2y)/dx^2)^3 + ((d^3y)/dx^3)^2y = x^2` is of ______ 


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


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


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


The degree of the differential equation `("d"^2y)/("d"x^2) + "e"^((dy)/(dx))` = 0 is ______.


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

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


Write the degree of the differential equation (y''')2 + 3(y") + 3xy' + 5y = 0


Determine the order and degree of the following differential equation:

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


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 ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×