Advertisements
Advertisements
प्रश्न
Determine the order and degree of the following differential equation:
`("d"^2"y")/"dx"^2 + "x"("dy"/"dx")` + y = 2 sin x
उत्तर
The given D.E. is
`("d"^2"y")/"dx"^2 + "x"("dy"/"dx")` + y = 2 sin x
This D.E. has highest order derivative `("d"^2"y")/"dx"^2` with power 1.
∴ the given D.E. is of order 2 and degree 1.
APPEARS IN
संबंधित प्रश्न
Write the degree of the differential equation `x^3((d^2y)/(dx^2))^2+x(dy/dx)^4=0`
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' + 5y = 0
Determine the order and degree (if defined) of the differential equation:
`(d^2y)/(dx^2)^2 + cos(dy/dx) = 0`
Determine the order and degree (if defined) of the differential equation:
y″ + (y′)2 + 2y = 0
The degree of the differential equation `((d^2y)/(dx^2))^3 + ((dy)/(dx))^2 + sin ((dy)/(dx)) + 1 = 0` is ______.
For the differential equation given below, indicate its order and degree (if defined).
`(d^2y)/dx^2 + 5x(dy/dx)^2 - 6y = log x`
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 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`
(y'')2 + (y')3 + sin y = 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 order of the differential equation
\[1 + \left( \frac{dy}{dx} \right)^2 = 7 \left( \frac{d^2 y}{d x^2} \right)^3\]
What is the degree of the following differential equation?
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 \[\left( \frac{d^2 y}{d x^2} \right)^2 - \left( \frac{dy}{dx} \right) = y^3\], is
Write the sum of the order and degree of the differential equation
\[\left( \frac{d^2 y}{{dx}^2} \right)^2 + \left( \frac{dy}{dx} \right)^3 + x^4 = 0 .\]
Determine the order and degree (if defined) of the following differential equation:-
y"' + 2y" + y' = 0
Determine the order and degree (if defined) of the following differential equation:-
(y"')2 + (y")3 + (y')4 + y5 = 0
Determine the order and degree (if defined) of the following differential equation:-
y"' + y2 + ey' = 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
In the following verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation:-
`y=sqrt(1+x^2)` `y'=(xy)/(1+x^2)`
Write the order and degree of the differential equation `((d^4"y")/(d"x"^4))^2 = [ "x" + ((d"y")/(d"x"))^2]^3`.
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:
(y''')2 + 3y'' + 3xy' + 5y = 0
Determine the order and degree of the following differential equation:
`(("d"^3"y")/"dx"^3)^(1/2) - ("dy"/"dx")^(1/3) = 20`
Determine the order and degree of the following differential equation:
`"x" + ("d"^2"y")/"dx"^2 = sqrt(1 + (("d"^2"y")/"dx"^2)^2)`
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`
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.
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.
State the degree of differential equation `"e"^((dy)/(dx)) + (dy)/(dx)` = x
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
Order of highest derivative occurring in the differential equation is called the ______ of the differential equation
Order and degree of differential equation`(("d"^3y)/("d"x^3))^(1/6)`= 9 is ______
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
The degree of the differential equation `("d"^4"y")/"dx"^4 + sqrt(1 + ("dy"/"dx")^4)` = 0 is
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 `[1 + 1/("dy"/"dx")^2]^(5/3) = 5 ("d"^2y)/"dx"^2` are respectively.
The differential equation `x((d^2y)/dx^2)^3 + ((d^3y)/dx^3)^2y = x^2` is of ______
The order and degree of the differential equation `(dy/dx)^3 + ((d^3y)/dx^3) + xy = 0` 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 of the differential equation of all circles of radius r, having centre on X-axis and passing through the origin 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 of the differential equation of all circles of given radius a is ______.
Order of the differential equation representing the family of parabolas y2 = 4ax is ______.
Degree of the differential equation `sqrt(1 + ("d"^2y)/("d"x^2)) = x + "dy"/"dx"` is not defined.
The degree of the differential equation `(("d"^2y)/("d"x^2))^2 + (("d"y)/("d"x))^2 = xsin(("d"y)/("d"x))` is ______.
The degree of the differential equation `[1 + (("d"y)/("d"x))^2]^(3/2) = ("d"^2y)/("d"x^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 ______.
The order and degree of the differential equation `[1 + ((dy)/(dx))^2] = (d^2y)/(dx^2)` are ______.
The degree of the differential equation `sqrt(1 + (("d"y)/("d"x))^2)` = x is ______.
The degree of the differential equation `("d"^2"y")/("dx"^2) + 3("dy"/"dx")^2 = "x"^2 (("d"^2"y")/("dx"^2))^2` is:
Write the sum of the order and the degree of the following differential equation:
`d/(dx) (dy/dx)` = 5
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
If m and n, respectively, are the order and the degree of the differential equation `d/(dx) [((dy)/(dx))]^4` = 0, then m + n = ______.
Find the general solution of the following differential equation:
`(dy)/(dx) = e^(x-y) + x^2e^-y`
The degree of the differential equation `dy/dx - x = (y - x dy/dx)^-4` is ______.
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 equation `sqrt(dy/dx) - 4 dy/dx - 7x` = 0 are ______.
Find the order and degree of the differential equation
`sqrt(1 + 1/(dy/dx)^2) = ((d^2y)/(dx^2))^(3/2)`
