हिंदी

Determine the order and degree of the following differential equation: dydx=2sinx+3dydx

Advertisements
Advertisements

प्रश्न

Determine the order and degree of the following differential equation:

`(dy)/(dx) = (2sin x + 3)/(dy/dx)`

योग
Advertisements

उत्तर

The given Differential equation is

`(dy)/(dx) = (2sin x + 3)/((dy)/(dx))`

∴ `(dy/dx)^2` = 2 sin x + 3

This D.E. has highest order derivative `"dy"/"dx"` with power 2.

∴ The given D.E. is of order 1 and degree 2.

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 6: Differential Equations - Exercise 6.1 [पृष्ठ १९३]

वीडियो ट्यूटोरियलVIEW ALL [3]

संबंधित प्रश्न

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′)2 + 2y = 0


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

`(d^4y)/dx^4 - sin ((d^3y)/(dx^3)) = 0`


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`


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

(xy2 + x) dx + (y − x2y) dy = 0


\[5\frac{d^2 y}{d x^2} = \left\{ 1 + \left( \frac{dy}{dx} \right)^2 \right\}^{3/2}\]

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

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

\[\frac{dy}{dx} + e^y = 0\]

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

Define order of a differential equation.


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


The order of the differential equation whose general solution is given by y = c1 cos (2x + c2) − (c3 + c4) ax + c5 + c6 sin (x − c7) is


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 (if defined) of the following differential equation:-

y"' + y2 + ey' = 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:

`[1 + (dy/dx)^2]^(3/2) = 8(d^2y)/dx^2`


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.

`(y''')^2 + 2(y'')^2 + 6y' + 7y = 0`


Determine the order and degree of the following differential equations.

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


Fill in the blank:

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


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`


The order and degree of `((dy)/(dx))^3 - (d^3y)/(dx^3) + ye^x` = 0 are ______.


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


State whether the following statement is True or False:  

The degree of a differential equation `"e"^(-("d"y)/("d"x)) = ("d"y)/("d"x) + "c"` is not defined


Degree of the given differential equation

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


The degree of the differential equation `("d"^4"y")/"dx"^4 + sqrt(1 + ("dy"/"dx")^4)` = 0 is


The third order differential equation is ______ 


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 ______.


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 `("d"^2y)/("d"x^2) + "e"^((dy)/(dx))` = 0 is ______.


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


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


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


The order and degree of the differential equation `sqrt((dy)/(dx)) - 4 (dy)/(dx) - 7x = 0` are respectively ______.


The degree of the differential equation `((d^3y)/(dx^2))^4 + ((d^2y)/(dx^2))^5 + (dy)/(dx) + y = 0` is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×