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Order of highest derivative occurring in the differential equation is called the ______ of the differential equation - Mathematics and Statistics

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प्रश्न

Order of highest derivative occurring in the differential equation is called the ______ of the differential equation

रिक्त स्थान भरें

उत्तर

order 

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अध्याय 1.8: Differential Equation and Applications - Q.2

संबंधित प्रश्न

(xy2 + x) dx + (y − x2y) dy = 0


\[y = x\frac{dy}{dx} + a\sqrt{1 + \left( \frac{dy}{dx} \right)^2}\]

\[e^\frac{dy}{dx} = x + 1 ; y\left( 0 \right) = 3\]

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"' + y2 + ey' = 0


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:

`root(3)(1 +("dy"/"dx")^2) = ("d"^2"y")/"dx"^2`


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"^2"y")/"dx"^2 + 5 "dy"/"dx" + "y" = "x"^3`


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:

`x+ dy/dx = 1 + (dy/dx)^2`


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 whether the following statement is True or False: 

Order and degree of differential equation are always positive integers.


The order of the differential equation of all circles whose radius is 4, is ______.


The degree of the differential equation `("d"^2y)/("d"x^2) + (("d"y)/("d"x))^3 + 6y^5` = 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 ______.


The degree of the differential equation `((d^2y)/dx^2)^2 + (dy/dx)^3` = ax is 3.


The degree of the differential equation `[1 + (dy/dx)^2]^3 = ((d^2y)/(dx^2))^2` is ______.


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