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प्रश्न
Order of highest derivative occurring in the differential equation is called the degree of the differential equation
पर्याय
True
False
उत्तर
This statement is False.
Explanation:
The order of highest derivative occurring in the differential equation is called degree of the differential equation.
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संबंधित प्रश्न
For the given below, verify that the given function (implicit or explicit) is a solution to the corresponding differential equation.
xy = a ex + b e-x + x2 : `x (d^2y)/(dx^2) + 2 dy/dx - xy + x^2 - 2 = 0`
Write the order and degree of the differential equation
\[y = x\frac{dy}{dx} + a\sqrt{1 + \left( \frac{dy}{dx} \right)^2}\]
The degree of the differential equation \[\left( \frac{d^2 y}{d x^2} \right)^3 + \left( \frac{dy}{dx} \right)^2 + \sin\left( \frac{dy}{dx} \right) + 1 = 0\], is
Determine the order and degree (if defined) of the following differential equation:-
\[\left( \frac{ds}{dt} \right)^4 + 3s\frac{d^2 s}{d t^2} = 0\]
In the following verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation:-
y = cos x + C y' + sin x = 0
Fill in the blank:
The order of highest derivative occurring in the differential equation is called ___________ of the differential equation.
Find the order and degree of the following differential equation:
`x+ dy/dx = 1 + (dy/dx)^2`
Choose the correct alternative:
The order and degree of `(1 + (("d"y)/("d"x))^3)^(2/3) = 8 ("d"^3y)/("d"x^3)` are respectively
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 degree of the differential equation `("d"^2y)/("d"x^2) + 3("dy"/"dx")^2 = x^2 log(("d"^2y)/("d"x^2))` is ______.
Degree of the differential equation `sqrt(1 + ("d"^2y)/("d"x^2)) = x + "dy"/"dx"` is not defined.
The order and degree of the differential equation `[1 + ((dy)/(dx))^2] = (d^2y)/(dx^2)` are ______.
The degree of the differential equation `("d"^2y)/("d"x^2) + "e"^((dy)/(dx))` = 0 is ______.
y2 = (x + c)3 is the general solution of the differential equation ______.
The degree of the differential equation `((d^2y)/dx^2)^2 + (dy/dx)^3` = ax is 3.
Find the order and degree of the differential equation `(d^2y)/(dx^2) = root(3)(1 - (dy/dx)^4`
