Advertisements
Advertisements
प्रश्न
Write the degree of the differential equation `x^3((d^2y)/(dx^2))^2+x(dy/dx)^4=0`
उत्तर
The given differential equation is ` x^3((d^2y)/(dx^2))^2+x(dy/dx)^4=0`
The highest order derivative present in the given differential equation is `(d^2y)/(dx^2)` The power raised to `(d^2y)/(dx^2) ` is two. So, the degree of the given differential equation is 2.
APPEARS IN
संबंधित प्रश्न
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)` = cos 3x + sin 3x
Determine the order and degree (if defined) of the differential equation:
y′′′ + 2y″ + y′ = 0
Determine the order and degree (if defined) of the differential equation:
y′ + y = ex
For the differential equation given below, indicate its order and degree (if defined).
`(d^2y)/dx^2 + 5x(dy/dx)^2 - 6y = log x`
Define degree of a differential equation.
Write the order of the differential equation whose solution is y = a cos x + b sin x + c e−x.
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 degree of the differential equation \[\left( \frac{d^2 y}{d x^2} \right)^2 - \left( \frac{dy}{dx} \right) = y^3\], is
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 = x2 + 2x + C y' − 2x − 2 = 0
Determine the order and degree of the following differential equation:
`(("d"^2"y")/"dx"^2)^2 + cos ("dy"/"dx") = 0`
Choose the correct option from the given alternatives:
The order and degree of the differential equation `sqrt(1 + ("dy"/"dx")^2) = (("d"^2"y")/"dx"^2)^(3/2)` are respectively.
Determine the order and degree of the following differential equation:
`"dy"/"dx" = 3"y" + root(4)(1 + 5 ("dy"/"dx")^2)`
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.
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.
Find the order and degree of the following differential equation:
`[ (d^3y)/dx^3 + x]^(3/2) = (d^2y)/dx^2`
The differential equation of the family of curves y = ex (A cos x + B sin x). Where A and B are arbitary constants is ______.
The order and degree of the differential equation `[1 + ("dy"/"dx")^2]^2 = ("d"^2y)/("d"x^2)` respectively, are ______.
The degree of the differential equation `("dy"/"dx")^2 + (("d"^2y)/("d"x^2))^2` = 0 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"^2"y")/("dx"^2) + 3("dy"/"dx")^2 = "x"^2 (("d"^2"y")/("dx"^2))^2` is:
Determine the order and degree of the following differential equation:
`(d^2y)/(dx^2) + x((dy)/(dx)) + y` = 2 sin x
The degree of the differential equation `dy/dx - x = (y - x dy/dx)^-4` is ______.
The differential equation representing the family of curves y2 = `2c(x + sqrt(c))`, where c is a positive parameter, is of ______.
The order and degree of the differential equation `sqrt(dy/dx) - 4 dy/dx - 7x` = 0 are ______.
The sum of the order and the degree of the differential equation `d/dx[(dy/dx)^3]` is ______.
