मराठी
महाराष्ट्र राज्य शिक्षण मंडळएचएससी वाणिज्य (इंग्रजी माध्यम) इयत्ता १२ वी

Determine the order and degree of the following differential equations. (d2ydx2)2+(dydx)2=ax

Advertisements
Advertisements

प्रश्न

Determine the order and degree of the following differential equations.

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

बेरीज
Advertisements

उत्तर

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

By definition of order and degree,

Order : 2 ; Degree : 2

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 8: Differential Equation and Applications - Exercise 8.1 [पृष्ठ १६२]

APPEARS IN

बालभारती Mathematics and Statistics 1 (Commerce) [English] Standard 12 Maharashtra State Board
पाठ 8 Differential Equation and Applications
Exercise 8.1 | Q 1.2 | पृष्ठ १६२

संबंधित प्रश्‍न

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.

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


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

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

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 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


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" + 2y' + sin y = 0


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

y"' + y2 + ey' = 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`


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 equation:

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


Determine the order and degree of the following differential equation:

`(("d"^3"y")/"dx"^3)^(1/2) - ("dy"/"dx")^(1/3) = 20`


Determine the order and degree of the following differential equations.

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


Determine the order and degree of the following differential equations.

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


State the degree of differential equation `e^((dy)/(dx)) + (dy)/(dx)` = x


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 order of the differential equation of all circles of radius r, having centre on X-axis and passing through the origin 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 ______.


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) + (("d"y)/("d"x))^3 + 6y^5` = 0 is ______.


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


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


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


The order of the differential equation of all parabolas, whose latus rectum is 4a and axis parallel to the x-axis, is ______.


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


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


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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×