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प्रश्न
Define order of a differential equation.
उत्तर
Order of differential equation:
The order of a differential equation is the order of its highest order derivative that apears in the equation.
example: \[\frac{d^2 y}{d x^2} - 4\left( \frac{dy}{dx} \right) = 2y\]
order of the differential equation is 2.
APPEARS IN
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
For the differential equation given below, indicate its order and degree (if defined).
`((dy)/(dx))^3 -4(dy/dx)^2 + 7y = sin x`
For the differential equation given below, indicate its order and degree (if defined).
`(d^4y)/dx^4 - sin ((d^3y)/(dx^3)) = 0`
(xy2 + x) dx + (y − x2y) dy = 0
Write the degree of the differential equation
\[a^2 \frac{d^2 y}{d x^2} = \left\{ 1 + \left( \frac{dy}{dx} \right)^2 \right\}^{1/4}\]
Write the degree of the differential equation
\[\frac{d^2 y}{d x^2} + x \left( \frac{dy}{dx} \right)^2 = 2 x^2 \log \left( \frac{d^2 y}{d x^2} \right)\]
Write the order of the differential equation of the family of circles touching X-axis at the origin.
Write the order of the differential equation of all non-horizontal lines in a plane.
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 whose general solution is given by y = c1 cos (2x + c2) − (c3 + c4) ax + c5 + c6 sin (x − c7) is
Determine the order and degree (if defined) of the following differential equation:-
(y"')2 + (y")3 + (y')4 + y5 = 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^3y)/dx^3)^(1/6) = 9`
Fill in the blank:
Order and degree of a differential equation are always __________ integers.
State whether the following is True or False:
The order of highest derivative occurring in the differential equation is called degree of the differential equation.
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
State the degree of differential equation `"e"^((dy)/(dx)) + (dy)/(dx)` = x
The order and degree of `((dy)/(dx))^3 - (d^3y)/(dx^3) + ye^x` = 0 are ______.
The power of highest ordered derivative when all the derivatives are made free from negative and/or fractional indices if any is called ______ of the differential equation
The order of the differential equation of all circles which lie in the first quadrant and touch both the axes is ______.
The order of the differential equation of all circles of radius r, having centre on X-axis and passing through the origin is ______.
Order of the differential equation representing the family of ellipses having centre at origin and foci on x-axis is two.
Degree of the differential equation `sqrt(1 + ("d"^2y)/("d"x^2)) = x + "dy"/"dx"` is not defined.
The degree of the differential equation `[1 + (("d"y)/("d"x))^2]^(3/2) = ("d"^2y)/("d"x^2)` 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 `[1 + ((dy)/(dx))^2] = (d^2y)/(dx^2)` are ______.
The order of differential equation `2x^2 (d^2y)/(dx^2) - 3 (dy)/(dx) + y` = 0 is
Write the degree of the differential equation (y''')2 + 3(y") + 3xy' + 5y = 0
y2 = (x + c)3 is the general solution of the differential equation ______.
Determine the order and degree of the following differential equation:
`(d^2y)/(dx^2) + x((dy)/(dx)) + y` = 2 sin x
The degree and order of the differential equation `[1 + (dy/dx)^3]^(7/3) = 7((d^2y)/(dx^2))` respectively are ______.
The order and degree of the differential eqµation whose general solution is given by `(d^2y)/(dx^2) + (dy/dx)^50` = In `((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?
