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प्रश्न
Fill in the blank:
Order and degree of a differential equation are always __________ integers.
उत्तर
Order and degree of a differential equation are always positive integers.
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संबंधित प्रश्न
Determine the order and degree (if defined) of the differential equation:
y′ + y = ex
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.
`y = e^x (acos x + b sin x) : (d^2y)/(dx^2) - 2 dy/dx + 2y = 0`
Write the order and degree of the differential equation
\[y = x\frac{dy}{dx} + a\sqrt{1 + \left( \frac{dy}{dx} \right)^2}\]
Write the order of the differential equation whose solution is y = a cos x + b sin x + c e−x.
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 (if defined) of the following differential equation:-
\[\left( \frac{ds}{dt} \right)^4 + 3s\frac{d^2 s}{d t^2} = 0\]
Determine the order and degree (if defined) of the following differential equation:-
y" + (y')2 + 2y = 0
In the following verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation:-
y = x2 + 2x + C y' − 2x − 2 = 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 `[ 1+ (dy/dx)^3]^(2/3) = 8 (d^3y)/dx^3` are respectively.
Order and degree of differential equation are always ______ integers
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.
The order and degree of the differential equation `[1 + ["dy"/"dx"]^3]^(7/3) = 7 (("d"^2"y")/"dx"^2)` are respectively.
The order and degree of the differential equation `("d"^2"y")/"dx"^2 + (("d"^3"y")/"dx"^3) + x^(1/5) = 0` are respectively.
Degree of the differential equation `sqrt(1 + ("d"^2y)/("d"x^2)) = x + "dy"/"dx"` is not defined.
If m and n, respectively, are the order and the degree of the differential equation `d/(dx) [((dy)/(dx))]^4` = 0, then m + n = ______.
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?
