मराठी

For the differential equation given below, indicate its order and degree (if defined). d2ydx2+5x(dydx)2-6y=logx

Advertisements
Advertisements

प्रश्न

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

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

बेरीज
Advertisements

उत्तर

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

In this differential equation, the highest derivative order is `(d^2y)/dx^2.`

Therefore, the order of the equation is 2, and the Degree is 1.

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 9: Differential Equations - Exercise 9.7 [पृष्ठ ४१९]

APPEARS IN

एनसीईआरटी Mathematics Part 1 and 2 [English] Class 12
पाठ 9 Differential Equations
Exercise 9.7 | Q 1.1 | पृष्ठ ४१९

व्हिडिओ ट्यूटोरियलVIEW ALL [3]

संबंधित प्रश्‍न

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

( y′′′) + (y″)3 + (y′)4 + y5 = 0


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

y″ + 2y′ + sin y = 0


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


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

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

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

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

Define degree of a differential equation.


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


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:-

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


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

(y"')2 + (y")3 + (y')4 + y5 = 0


Determine the order and degree of the following differential equation:

`("d"^2"y")/"dx"^2 + ("dy"/"dx")^2 + 7"x" + 5 = 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.

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


Determine the order and degree of the following differential equations.

`dy/dx = 7 (d^2y)/dx^2`


Choose the correct alternative.

The order and degree of `[ 1+ (dy/dx)^3]^(2/3) = 8 (d^3y)/dx^3` are respectively.


Fill in the blank:

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


Select and write the correct alternative from the given option for the question

The order and degree of `(1 + (("d"y)/("d"x))^3)^(2/3) = 8 ("d"^3y)/("d"x^3)` are respectively


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


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


The third order differential equation is ______ 


The order and degree of `(("n + 1")/"n")("d"^4"y")/"dx"^4 = ["n" + (("d"^2"y")/"dx"^2)^4]^(3//5)` are respectively.


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


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


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


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


The order and degree of the differential equation `[1 + ((dy)/(dx))^3]^(2/3) = 8((d^3y)/(dx^3))` are respectively ______.


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


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 `dy/dx - x = (y - x dy/dx)^-4` is ______.


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


For the differential equation \[y''' + y^{2} + e^{y'} = 0\], is the degree defined?


Based on the differential equation \[\left(\frac{d^{3}y}{dx^{3}}\right)^{2} + 5\frac{dy}{dx} = \sin(x)\], what is the degree?


Which of the following statements is true regarding order and degree of differential equations?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×