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 - Mathematics

Question

Write the order and the degree of the following differential equation: $x^{3} {(\frac{d^{2} y}{d x^{2}})}^{2} + x {(\frac{d y}{d x})}^{4} = 0$

Sum

Solution

Order is the highest order derivative present in the differential equation
And the degree is the power of the highest order derivative.

We have given the differential equation:

$x^{3} {(\frac{d^{2} y}{d x^{2}})}^{2} + x {(\frac{d y}{d x})}^{4} = 0$

Here, order is 2 and degree is 2.

shaalaa.com

Order and Degree of a Differential Equation

Is there an error in this question or solution?

Q 2 Q 1 Q 3

2018-2019 (March) 65/1/3

APPEARS IN

2018-2019 (March) 65/1/3 (with solutions)

Q 2 | 1 mark

Video TutorialsVIEW ALL [3]

view
Video Tutorials For All Subjects
Order and Degree of a Differential Equation

video tutorial00:03:35
Order and Degree of a Differential Equation

video tutorial00:34:57
Order and Degree of a Differential Equation

video tutorial00:26:33

RELATED QUESTIONS

Write the degree of the differential equation $x^{3} {(\frac{d^{2} y}{{d x}^{2}})}^{2} + x {(\frac{d y}{d x})}^{4} = 0$

Determine the order and degree (if defined) of the differential equation:

$\frac{d^{2} y}{{d x}^{2}}$ = cos 3x + sin 3x

The degree of the differential equation ${(\frac{d^{2} y}{{d x}^{2}})}^{3} + {(\frac{d y}{d x})}^{2} + \sin (\frac{d y}{d x}) + 1 = 0$ is ______.

For the given below, verify that the given function (implicit or explicit) is a solution to the corresponding differential equation.

xy = a e^x + b e^-x + x² : $x \frac{d^{2} y}{{d x}^{2}} + 2 \frac{d y}{d x} - x y + x^{2} - 2 = 0$

Write the order of the differential equation
$1 + {(\frac{d y}{d x})}^{2} = 7 {(\frac{d^{2} y}{d x^{2}})}^{3}$

Write the order of the differential equation of the family of circles touching X-axis at the origin.

Write the degree of the differential equation $\frac{d^{2} y}{d x^{2}} + 3 {(\frac{d y}{d x})}^{2} = x^{2} \log (\frac{d^{2} y}{d x^{2}})$

Determine the order and degree of the following differential equation:

$\sqrt[3]{1 + {(\frac{dy}{dx})}^{2}} = \frac{d^{2} y}{{dx}^{2}}$

Determine the order and degree of the following differential equation:

$\frac{d^{2} y}{{dx}^{2}} + {(\frac{dy}{dx})}^{2} + 7 x + 5 = 0$

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.

Find the order and degree of the following differential equation:

$x + \frac{d y}{d x} = 1 + {(\frac{d y}{d x})}^{2}$

The order and degree of ${(\frac{d y}{d x})}^{3} - \frac{d^{3} y}{{d x}^{3}} + y e^{x}$ = 0 are ______.

Choose the correct alternative:

The order and degree of ${(1 + {(\frac{d y}{d x})}^{3})}^{\frac{2}{3}} = 8 \frac{d^{3} y}{d x^{3}}$ are respectively

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

Order and degree of differential equation ${(\frac{d^{3} y}{d x^{3}})}^{\frac{1}{6}}$ = 9 is ______

State whether the following statement is True or False:

Order and degree of differential equation $x \frac{d^{3} y}{d x^{3}} + 6 {(\frac{d^{2} y}{d x^{2}})}^{2} + y$ = 0 is (2, 2)

The order and degree of the differential equation ${[1 + \frac{1}{{(\frac{dy}{dx})}^{2}}]}^{\frac{5}{3}} = 5 \frac{d^{2} y}{{dx}^{2}}$ are respectively.

The order of the differential equation of all circles which lie in the first quadrant and touch both the axes is ______.

The degree of the differential equation ${(1 + \frac{dy}{dx})}^{3} = {(\frac{d^{2} y}{d x^{2}})}^{2}$ is ______.

The order and degree of the differential equation ${[1 + {(\frac{dy}{dx})}^{2}]}^{2} = \frac{d^{2} y}{d x^{2}}$ respectively, are ______.

The order and degree of the differential equation $\frac{d^{2} y}{d x^{2}} + {(\frac{d y}{d x})}^{\frac{1}{4}} + x^{\frac{1}{5}}$ = 0, respectively, are ______.

The degree of the differential equation $\frac{d^{2} y}{d x^{2}} + e^{\frac{d y}{d x}}$ = 0 is ______.

Write the degree of the differential equation (y''')² + 3(y") + 3xy' + 5y = 0

The differential equation representing the family of curves y² = $2 c (x + \sqrt{c})$ , where c is a positive parameter, is of ______.

The degree of the differential equation ${(\frac{d^{2} y}{{d x}^{2}})}^{2} + {(\frac{d y}{d x})}^{3}$ = a^x is 3.

The order and the degree of the differential equation ${(1 + 3 \frac{d y}{d x})}^{2} = 4 \frac{d^{3} y}{{d x}^{3}}$ respectively are ______.

Find the order and degree of the differential equation

$\sqrt{1 + \frac{1}{{(\frac{d y}{d x})}^{2}}} = {(\frac{d^{2} y}{{d x}^{2}})}^{\frac{3}{2}}$

Assertion: Degree of the differential equation: $a {(\frac{d y}{d x})}^{2} + b \frac{d x}{d y} = c$ , is 3

Reason: If each term involving derivatives of a differential equation is a polynomial (or can be expressed as polynomial) then highest exponent of the highest order derivative is called the degree of the differential equation.

Which of the following is correct?

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 - Mathematics

Advertisements

Advertisements

Question

Solution

APPEARS IN

Video TutorialsVIEW ALL [3]

RELATED QUESTIONS

Select a course

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 - Mathematics

Advertisements

Advertisements

Question

SolutionShow Solution

APPEARS IN

Video TutorialsVIEW ALL [3]

RELATED QUESTIONS

Select a course

Solution