मराठी

(Y'')2 + (Y')3 + Sin Y = 0

Advertisements
Advertisements

प्रश्न

(y'')2 + (y')3 + sin y = 0

Advertisements

उत्तर

\[\left( y'' \right)^2 + \left( y' \right)^3 + \sin y = 0\]
In this differential equation, the order of the highest order derivative is 2 and its power is 2. So, the order of the differential equation is 2 and its degree is 2.
It is a non-linear differential equation, as its degree is 2, which is more than 1.
shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 21: Differential Equations - Exercise 22.01 [पृष्ठ ५]

APPEARS IN

आर.डी. शर्मा Mathematics Volume 1 and 2 [English] Class 12
पाठ 21 Differential Equations
Exercise 22.01 | Q 22 | पृष्ठ ५

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:

y′′′ + 2y″ + 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`


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

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

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

The degree of the differential equation \[\frac{d^2 y}{d x^2} + e^\frac{dy}{dx} = 0\]


The degree of the differential equation \[\left( \frac{d^2 y}{d x^2} \right)^2 - \left( \frac{dy}{dx} \right) = y^3\], is


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

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


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

(y"')2 + (y")3 + (y')4 + y5 = 0


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:

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


Determine the order and degree of the following differential equation:

`"dy"/"dx" = 3"y" + root(4)(1 + 5 ("dy"/"dx")^2)`


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.


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 power of the highest ordered derivative when all the derivatives are made free from negative and / or fractional indices if any is called order of the differential equation.


Choose the correct alternative:

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


Order and degree of differential equation are always ______ integers


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


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


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


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 and degree of the differential equation `("d"^2"y")/"dx"^2 + (("d"^3"y")/"dx"^3) + x^(1/5) = 0` are respectively.


The degree of the differential equation `("d"^2y)/("d"x^2) + (("d"y)/("d"x))^3 + 6y^5` = 0 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:


Write the degree of the differential equation (y''')2 + 3(y") + 3xy' + 5y = 0


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


The degree of the differential equation `dy/dx - x = (y - x dy/dx)^-4` is ______.


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?


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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×