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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

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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

shaalaa.com
  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' + 5y = 0


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

\[\frac{dy}{dx} + e^y = 0\]

\[e^\frac{dy}{dx} = x + 1 ; y\left( 0 \right) = 3\]

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

Define order of a differential equation.


Write the order of the differential equation
\[1 + \left( \frac{dy}{dx} \right)^2 = 7 \left( \frac{d^2 y}{d x^2} \right)^3\]


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


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 option from the given alternatives:

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


Determine the order and degree of the following differential equations.

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


Fill in the blank:

Order and degree of a differential equation are always __________ integers.


Find the order and degree of the following differential equation:

`[ (d^3y)/dx^3 + x]^(3/2) = (d^2y)/dx^2`


Select and write the correct alternative from the given option for the question

The order and degree of `(("d"y)/("d"x))^3 - ("d"^3y)/("d"x^3) + y"e"^x` = 0 are respectively


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


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 and degree of `(("n + 1")/"n")("d"^4"y")/"dx"^4 = ["n" + (("d"^2"y")/"dx"^2)^4]^(3//5)` are respectively.


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


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.


If m and n, respectively, are the order and the degree of the differential equation `d/(dx) [((dy)/(dx))]^4` = 0, then m + n = ______.


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


In the differential equation \[\frac{d^{2}y}{dx^{2}} + \left(\frac{dy}{dx}\right)^{3} - y = 0\], what are the order and degree respectively?


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