English

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 fr - Mathematics and Statistics

Advertisements
Advertisements

Question

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

Options

  • True

  • False

MCQ
True or False

Solution

True

shaalaa.com
  Is there an error in this question or solution?
Chapter 1.8: Differential Equation and Applications - Q.3

RELATED QUESTIONS

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

y' + 5y = 0


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

( y′′′) + (y″)3 + (y′)4 + y5 = 0


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


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

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

(y'')2 + (y')3 + sin y = 0


Define degree of a differential equation.


Write the order of the differential equation of the family of circles touching X-axis at the origin.


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


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 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:-

(y"')2 + (y")3 + (y')4 + y5 = 0


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 + "x"("dy"/"dx")` + y = 2 sin x


Determine the order and degree of the following differential equation:

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


Choose the correct alternative.

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


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


The order of the differential equation of all circles whose radius is 4, is ______.


The third order differential equation is ______ 


If m and n are the order and degree of the differential equation `((d^3y)/(dx^3))^6+5((d^3y)/(dx^3))^4/((d^4y)/(dx^4))+(d^4y)/(dx^4)=x^3-1,` then ______.


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


Find the general solution of the following differential equation:

`(dy)/(dx) = e^(x-y) + x^2e^-y`


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


The order and degree of the differential eqµation whose general solution is given by `(d^2y)/(dx^2) + (dy/dx)^50` = In `((d^2y)/dx^2)` respectively, are ______.


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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×