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प्रश्न
Fill in the blank:
The power of the highest ordered derivative when all the derivatives are made free from negative and / or fractional indices if any is called __________ of the differential equation.
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उत्तर
The power of the highest ordered derivative when all the derivatives are made free from negative and/or fractional indices if any is called degree of the differential equation.
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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
Determine the order and degree (if defined) of the differential equation:
y″ + 2y′ + sin y = 0
For the differential equation given below, indicate its order and degree (if defined).
`(d^4y)/dx^4 - sin ((d^3y)/(dx^3)) = 0`
For the given below, verify that the given function (implicit or explicit) is a solution to the corresponding differential equation.
`x^2 = 2y^2 log y : (x^2 + y^2) dy/dx - xy = 0`
Write the degree of the differential equation x \[\left( \frac{d^2 y}{d x^2} \right)^3 + y \left( \frac{dy}{dx} \right)^4 + x^3 = 0\]
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
The order of the differential equation satisfying
\[\sqrt{1 - x^4} + \sqrt{1 - y^4} = a\left( x^2 - y^2 \right)\] is
The order of the differential equation \[2 x^2 \frac{d^2 y}{d x^2} - 3\frac{dy}{dx} + y = 0\], is
Determine the order and degree of the following differential equation:
`root(3)(1 +("dy"/"dx")^2) = ("d"^2"y")/"dx"^2`
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 equation:
`("d"^2"y")/"dx"^2 + 5 "dy"/"dx" + "y" = "x"^3`
Determine the order and degree of the following differential equations.
`(y''')^2 + 2(y'')^2 + 6y' + 7y = 0`
Determine the order and degree of the following differential equations.
`dy/dx = 7 (d^2y)/dx^2`
Fill in the blank:
Order and degree of a differential equation are always __________ integers.
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.
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
Order and degree of differential equation`(("d"^3y)/("d"x^3))^(1/6)`= 9 is ______
State whether the following statement is True or False:
Order and degree of differential equation are always positive integers.
Degree of the given differential equation
`(("d"^3"y")/"dx"^2)^2 = (1 + "dy"/"dx")^(1/3)` is
The third order differential equation is ______
The degree of the differential equation `("d"^2y)/("d"x^2) + 3("dy"/"dx")^2 = x^2 log(("d"^2y)/("d"x^2))` is ______.
The order and degree of the differential equation `[1 + ("dy"/"dx")^2]^2 = ("d"^2y)/("d"x^2)` respectively, are ______.
Order of the differential equation representing the family of parabolas y2 = 4ax is ______.
The degree of the differential equation `("d"^2y)/("d"x^2) + (("d"y)/("d"x))^3 + 6y^5` = 0 is ______.
The order and degree of the differential equation `(("d"^3y)/("d"x^3))^2 - 3 ("d"^2y)/("d"x^2) + 2(("d"y)/("d"x))^4` = y4 are ______.
The order of differential equation `2x^2 (d^2y)/(dx^2) - 3 (dy)/(dx) + y` = 0 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?
