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प्रश्न
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
विकल्प
True
False
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उत्तर
True
संबंधित प्रश्न
The order of the differential equation `2x^2 (d^2y)/(dx^2) - 3 (dy)/(dx) + y = 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 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`
Write the degree of the differential equation \[\frac{d^2 y}{d x^2} + 3 \left( \frac{dy}{dx} \right)^2 = x^2 \log\left( \frac{d^2 y}{d x^2} \right)\]
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 \[\frac{d^2 y}{d x^2} + e^\frac{dy}{dx} = 0\]
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"' + 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
Determine the order and degree of the following differential equation:
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Determine the order and degree of the following differential equations.
`((d^2y)/(dx^2))^2 + ((dy)/(dx))^2 =a^x `
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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.
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Order and degree of differential equation are always ______ integers
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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 `(("d"^3y)/("d"x^3))^2 - 3 ("d"^2y)/("d"x^2) + 2(("d"y)/("d"x))^4` = y4 are ______.
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The order of differential equation `2x^2 (d^2y)/(dx^2) - 3 (dy)/(dx) + y` = 0 is
The degree of the differential equation `dy/dx - x = (y - x dy/dx)^-4` is ______.
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The sum of the order and the degree of the differential equation `d/dx[(dy/dx)^3]` is ______.
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For the differential equation \[y''' + y^{2} + e^{y'} = 0\], is the degree defined?
Why is the degree of the differential equation \[y'' + \sin(y') = 0\] not defined?
