Advertisements
Advertisements
Question
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)`
Advertisements
Solution
The given D.E. is
`("d"^2"y")/"dx"^2 + "dy"/"dx" + "x" = sqrt(1 + ("d"^3"y")/"dx"^3)`
On squaring both sides, we get
`(("d"^2"y")/"dx"^2 + "dy"/"dx" + "x")^2 = 1 + ("d"^3"y")/"dx"^3`
This D.E. has highest order derivative `("d"^3"y")/"dx"^3` with power 1.
∴ the given D.E. has order 3 and degree 1.
APPEARS IN
RELATED QUESTIONS
Determine the order and degree (if defined) of the differential equation:
y′′′ + 2y″ + y′ = 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`
(y'')2 + (y')3 + sin y = 0
Write the order of the differential equation
\[1 + \left( \frac{dy}{dx} \right)^2 = 7 \left( \frac{d^2 y}{d x^2} \right)^3\]
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 degree of the differential equation \[x^3 \left( \frac{d^2 y}{d x^2} \right)^2 + x \left( \frac{dy}{dx} \right)^4 = 0\]
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
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
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
Determine the order and degree of the following differential equation:
`("d"^2"y")/"dx"^2 + "x"("dy"/"dx")` + y = 2 sin x
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:
`("d"^2"y")/"dx"^2 + 5 "dy"/"dx" + "y" = "x"^3`
Determine the order and degree of the following differential equation:
`("d"^4"y")/"dx"^4 + sin ("dy"/"dx") = 0`
Determine the order and degree of the following differential equations.
`(d^2x)/(dt^2)+((dx)/(dt))^2 + 8=0`
Determine the order and degree of the following differential equations.
`(d^4y)/dx^4 + [1+(dy/dx)^2]^3 = 0`
Determine the order and degree of the following differential equations.
`sqrt(1+1/(dy/dx)^2) = (dy/dx)^(3/2)`
Determine the order and degree of the following differential equations.
`((d^3y)/dx^3)^(1/6) = 9`
State whether the following is True or False:
The degree of the differential equation `e^((dy)/(dx)) = dy/dx +c` is not defined.
Select and write the correct alternative from the given option for the question
The order and degree of `(1 + (("d"y)/("d"x))^3)^(2/3) = 8 ("d"^3y)/("d"x^3)` 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 ______.
Order and degree of differential equation are always ______ integers
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
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
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 degree of the differential equation `("d"^4"y")/"dx"^4 + sqrt(1 + ("dy"/"dx")^4)` = 0 is
The order of the differential equation of all circles whose radius is 4, is ______.
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.
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 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
The order and degree of the differential equation `sqrt((dy)/(dx)) - 4 (dy)/(dx) - 7x = 0` are respectively ______.
For the differential equation \[y''' + y^{2} + e^{y'} = 0\], what is the order?
