Advertisements
Advertisements
प्रश्न
Write the order of the differential equation of all non-horizontal lines in a plane.
Advertisements
उत्तर
The equation of the non - horizontal lines in a plane is
\[y = mx + c, \]
where m is the slope and c is the intercept on y - axis .
Differentiating with respect to x, we get
\[\frac{dy}{dx} = m\]
\[ \Rightarrow \frac{d^2 y}{d x^2} = 0\]
This is the required differential equation .
Here, we observe that the order of the required differential equation is 2 .
APPEARS IN
संबंधित प्रश्न
Determine the order and degree (if defined) of the differential equation:
`(d^2y)/(dx^2)` = cos 3x + sin 3x
Determine the order and degree (if defined) of the differential equation:
y″ + (y′)2 + 2y = 0
For the differential equation given below, indicate its order and degree (if defined).
`((dy)/(dx))^3 -4(dy/dx)^2 + 7y = sin x`
(y'')2 + (y')3 + sin y = 0
Define order of a differential equation.
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 x \[\left( \frac{d^2 y}{d x^2} \right)^3 + y \left( \frac{dy}{dx} \right)^4 + x^3 = 0\]
Write the degree of the differential equation \[\left( \frac{d^2 y}{d x^2} \right)^2 + \left( \frac{dy}{dx} \right)^2 = x\sin\left( \frac{dy}{dx} \right)\]
The order of the differential equation \[2 x^2 \frac{d^2 y}{d x^2} - 3\frac{dy}{dx} + y = 0\], 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"')2 + (y")3 + (y')4 + y5 = 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
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
Find the order and the degree of the differential equation `x^2 (d^2y)/(dx^2) = { 1 + (dy/dx)^2}^4`
Determine the order and degree of the following differential equation:
`(dy)/(dx) = (2sin x + 3)/(dy/dx)`
Determine the order and degree of the following differential equation:
`("d"^2"y")/"dx"^2 + "dy"/"dx" + "x" = sqrt(1 + ("d"^3"y")/"dx"^3)`
Determine the order and degree of the following differential equation:
`(("d"^2"y")/"dx"^2)^2 + cos ("dy"/"dx") = 0`
Determine the order and degree of the following differential equation:
`"dy"/"dx" = 3"y" + root(4)(1 + 5 ("dy"/"dx")^2)`
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.
`((d^3y)/dx^3)^(1/6) = 9`
State whether the following statement is true or false:
Order and degree of a differential equation are always positive 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.
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 whether the following statement is True or False:
Order and degree of differential equation are always positive integers.
Order of highest derivative occurring in the differential equation is called the degree of the differential equation
Degree of the given differential equation
`(("d"^3"y")/"dx"^2)^2 = (1 + "dy"/"dx")^(1/3)` is
The order and degree of the differential equation `[1 + 1/("dy"/"dx")^2]^(5/3) = 5 ("d"^2y)/"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.
The order of the differential equation whose general solution is given by `y=C_(1)e^(2x+C_2)+C_3e^x+C_4sin(x+C_5)` 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] = (d^2y)/(dx^2)` are ______.
The degree of the differential equation `("d"^2y)/("d"x^2) + "e"^((dy)/(dx))` = 0 is ______.
The degree of differential equation `((d^2y)/(dx^2))^3 + ((dy)/(dx))^2 + sin((dy)/(dx)) + 1` = 0 is:
The order of differential equation `2x^2 (d^2y)/(dx^2) - 3 (dy)/(dx) + y` = 0 is
The degree of the differential equation `[1 + (dy/dx)^2]^3 = ((d^2y)/(dx^2))^2` is ______.
The sum of the degree and order of the differential equation \[\sqrt{\frac{\mathrm{d}^{2}y}{\mathrm{d}x^{2}}}=\sqrt[5]{\frac{\mathrm{d}y}{\mathrm{d}x}-5}\] is
