English

Degree of the differential equation dddydx1+d2ydx2=x+dydx is not defined.

Advertisements
Advertisements

Question

Degree of the differential equation `sqrt(1 + ("d"^2y)/("d"x^2)) = x + "dy"/"dx"` is not defined.

Options

  • True

  • False

MCQ
True or False
Advertisements

Solution

This statement is True.

Explanation:

Because it is not a polynomial equation in its derivatives.

shaalaa.com
  Is there an error in this question or solution?
Chapter 9: Differential Equations - Solved Examples [Page 191]

APPEARS IN

NCERT Exemplar Mathematics Exemplar [English] Class 12
Chapter 9 Differential Equations
Solved Examples | Q 23. (ii) | Page 191

RELATED QUESTIONS

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 = ex


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


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).

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


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

\[2\frac{d^2 y}{d x^2} + 3\sqrt{1 - \left( \frac{dy}{dx} \right)^2 - y} = 0\]

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


What is the degree of the following differential equation?

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

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


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"' + 2y" + y' = 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 equations.

`(d^4y)/dx^4 + [1+(dy/dx)^2]^3 = 0`


Choose the correct alternative.

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


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.


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 and degree of differential equation are always ______ integers


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


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


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


The order and degree of the differential equation `[1 + ["dy"/"dx"]^3]^(7/3) = 7 (("d"^2"y")/"dx"^2)` are respectively.


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


The order of the differential equation of all circles of given radius a is ______.


Order of the differential equation representing the family of parabolas y2 = 4ax is ______.


Order of the differential equation representing the family of ellipses having centre at origin and foci on x-axis is two.


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


Polio drops are delivered to 50 K children in a district. The rate at which polio drops are given is directly proportional to the number of children who have not been administered the drops. By the end of 2nd week half the children have been given the polio drops. How many will have been given the drops by the end of 3rd week can be estimated using the solution to the differential equation `"dy"/"dx" = "k"(50 - "y")` where x denotes the number of weeks and y the number of children who have been given the drops.

State the order of the above given differential equation.


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


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

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


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


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


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


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


What is the key difference between order and degree of a differential equation?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×