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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

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प्रश्न

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

विकल्प

  • True

  • False

MCQ
सत्य या असत्य
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उत्तर

True

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  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 1.8: Differential Equation and Applications - Q.3

संबंधित प्रश्न

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

( y′′′) + (y″)3 + (y′)4 + y5 = 0


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

y′′′ + 2y″ + y′ = 0


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

y″ + 2y′ + sin y = 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`


\[s^2 \frac{d^2 t}{d s^2} + st\frac{dt}{ds} = s\]

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

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

\[y = px + \sqrt{a^2 p^2 + b^2},\text{ where p} = \frac{dy}{dx}\]

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


The degree of the differential equation \[\left\{ 5 + \left( \frac{dy}{dx} \right)^2 \right\}^{5/3} = x^5 \left( \frac{d^2 y}{d x^2} \right)\], is


If p and q are the order and degree of the differential equation \[y\frac{dy}{dx} + x^3 \frac{d^2 y}{d x^2} + xy\] = cos x, then


The order of the differential equation \[2 x^2 \frac{d^2 y}{d x^2} - 3\frac{dy}{dx} + y = 0\], is


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

\[\left( \frac{d^2 y}{{dx}^2} \right)^2 + \left( \frac{dy}{dx} \right)^3 + x^4 = 0 .\]


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:

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


Choose the correct alternative.

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


Find the order and degree of the following differential equation:

`x+ dy/dx = 1 + (dy/dx)^2`


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


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


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


The order of the differential equation whose general solution is given by `y=C_(1)e^(2x+C_2)+C_3e^x+C_4sin(x+C_5)` 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 degree of the differential equation `("dy"/"dx")^2 + (("d"^2y)/("d"x^2))^2` = 0 is ______.


The order and degree of the differential equation `("d"^2y)/("d"x^2) + (("d"y)/("d"x))^(1/4) + x^(1/5)` = 0, respectively, are ______.


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


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 differential equation representing the family of curves y2 = `2c(x + sqrt(c))`, where c is a positive parameter, is of ______.


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


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?


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