हिंदी

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

Advertisements
Advertisements

प्रश्न

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

y"' + 2y" + y' = 0

टिप्पणी लिखिए
योग

उत्तर

y"' + 2y" + y' = 0

The highest order derivative in the given equation is y''' and its power is 1.

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

i.e., Order = 3 and degree = 1

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 22: Differential Equations - Revision Exercise [पृष्ठ १४४]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 12
अध्याय 22 Differential Equations
Revision Exercise | Q 1.2 | पृष्ठ १४४

वीडियो ट्यूटोरियलVIEW ALL [3]

संबंधित प्रश्न

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

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


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

`((ds)/(dt))^4 + 3s  (d^2s)/(dt^2) = 0`


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

y′ + y = ex


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

y″ + (y′)2 + 2y = 0


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

`y = xsin 3x   :   (d^2y)/(dx^2) + 9y - 6 cos 3x = 0`


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

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

Define degree of a differential equation.


Write the order of the differential equation
\[1 + \left( \frac{dy}{dx} \right)^2 = 7 \left( \frac{d^2 y}{d x^2} \right)^3\]


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


Write the degree of the differential equation \[x^3 \left( \frac{d^2 y}{d x^2} \right)^2 + x \left( \frac{dy}{dx} \right)^4 = 0\]


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 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 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 `


Determine the order and degree of the following differential equations.

`((d^3y)/dx^3)^(1/6) = 9`


Fill in the blank:

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


State whether the following is True or False:

The order of highest derivative occurring in the differential equation is called degree of the differential equation.


State whether the following is True or False:

The degree of the differential equation `e^((dy)/(dx)) = dy/dx +c` is not defined.


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


Order and degree of differential equation`(("d"^3y)/("d"x^3))^(1/6)`= 9 is ______


State whether the following statement is True or False: 

Order and degree of differential equation are always positive 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


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


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


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


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


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


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

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


The degree of differential equation `((d^2y)/(dx^2))^3 + ((dy)/(dx))^2 + sin((dy)/(dx)) + 1` = 0 is:


Find the general solution of the following differential equation:

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


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


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


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×