मराठी

Determine the Order and Degree (If Defined) of the Following Differential Equation:- Y"' + Y2 + Ey' = 0

Advertisements
Advertisements

प्रश्न

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

y"' + y2 + ey' = 0

टीपा लिहा
बेरीज
Advertisements

उत्तर

y"' + y2 + ey' = 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.

This equation cannot be expressed as a polynomial of derivative.

Thus, the degree is not defined.

i.e., Order = 3 and degree is not defined.

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 21: Differential Equations - Revision Exercise [पृष्ठ १४४]

APPEARS IN

आर.डी. शर्मा Mathematics Volume 1 and 2 [English] Class 12
पाठ 21 Differential Equations
Revision Exercise | Q 1.7 | पृष्ठ १४४

व्हिडिओ ट्यूटोरियलVIEW ALL [3]

संबंधित प्रश्‍न

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


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

y″ + (y′)2 + 2y = 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`


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

`((dy)/(dx))^3 -4(dy/dx)^2 + 7y = sin x`


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`


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

`x^2 = 2y^2 log y : (x^2  + y^2) dy/dx - xy = 0`


\[\frac{d^3 y}{d x^3} + \left( \frac{d^2 y}{d x^2} \right)^3 + \frac{dy}{dx} + 4y = \sin x\]

\[\sqrt{1 - y^2} dx + \sqrt{1 - x^2} dx = 0\]

\[\frac{d^2 y}{d x^2} + 5x\left( \frac{dy}{dx} \right) - 6y = \log x\]

\[\left( \frac{dy}{dx} \right)^3 - 4 \left( \frac{dy}{dx} \right)^2 + 7y = \sin x\]

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


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


Write the order of the differential equation of all non-horizontal lines in a plane.


The order of the differential equation satisfying
\[\sqrt{1 - x^4} + \sqrt{1 - y^4} = a\left( x^2 - y^2 \right)\] is


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

y"' + 2y" + y' = 0


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`


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


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:

(y''')2 + 3y'' + 3xy' + 5y = 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`


State whether the following is True or False:

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


State whether the following statement is True or False: 

Order and degree of differential equation are always positive integers.


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 ______.


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 ______.


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

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


The order of differential equation `2x^2 (d^2y)/(dx^2) - 3 (dy)/(dx) + y` = 0 is


y2 = (x + c)3 is the general solution of the differential equation ______.


Determine the order and degree of the following differential equation:

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


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.


If `(a + bx)e^(y/x)` = x then prove that `x(d^2y)/(dx^2) = (a/(a + bx))^2`.


The sum of the degree and order of the differential equation \[\sqrt{\frac{\mathrm{d}^{2}y}{\mathrm{d}x^{2}}}=\sqrt[5]{\frac{\mathrm{d}y}{\mathrm{d}x}-5}\] is


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×