Find the order and degree of differential equation d 3 y d x 3 + d 2 y d x 2 3 + d y d x + 4 y = sin x . State also whether it is linear or non-linear

Given differential equation is d 3 y d x 3 + d 2 y d x 2 3 + d y d x + 4 y = sin x Here highest order derivative is d 3 y d x 3 and its highest power is 1 . Order: Highest order of derivative occurring in the given differential equation. Therefore, order of differential equation is 3 . Degree: The highest power of the highest order derivative present in the equation and the differential equation must be a polynomial equation in derivatives for the degree to be defined. Therefore, degree of differential equation is 1 . Since, the degree of differential coefficient d 2 y d x 2 has power 3 which is more than 1 Therefore, it is non-linear differential equation.

Find the order and degree of differential equation d 3 y d x 3 + d 2 y d x 2 3 + d y d x + 4 y = sin x . State also whether it is linear or non-linear

Given differential equation is d 3 y d x 3 + d 2 y d x 2 3 + d y d x + 4 y = sin x Here highest order derivative is d 3 y d x 3 and its highest power is 1 . Order: Highest order of derivative occurring in the given differential equation. Therefore, order of differential equation is 3 . Degree: The highest power of the highest order derivative present in the equation and the differential equation must be a polynomial equation in derivatives for the degree to be defined. Therefore, degree of differential equation is 1 . Since, the degree of differential coefficient d 2 y d x 2 has power 3 which is more than 1 Therefore, it is non-linear differential equation.

Find the order and degree of differential equation 5 d 2 y d x 2 = 1 + d y d x 2 3 2 . State also whether it is linear or non-linear.

Given differential equation is 5 d 2 y d x 2 = 1 + d y d x 2 3 2 Squaring both the sides 25 d 2 y d x 2 2 = 1 + d y d x 2 3 Here highest order derivative is d 2 y d x 2 and its highest power is 2 . Order: Highest order of derivative occurring in the given differential equation. Therefore, order of differential equation is 2 . Degree: The highest power of the highest order derivative present in the equation and the differential equation must be a polynomial equation in derivatives for the degree to be defined. Therefore, degree of differential equation is 2 . Since, the degree of differential equation is more than 1 . Therefore, it is non-linear differential equation.

Find the order and degree of differential equation d s d t 4 + 3 s d 2 s d t 2 = 0

Given differential equation is d s d t 4 + 3 s d 2 s d t 2 = 0 Here highest order derivative is d 2 s d t 2 and its highest power is 1 . Order: Highest order of derivative occurring in the given differential equation. Therefore, order of differential equation is 2 . Degree: The highest power of the highest order derivative present in the equation and the differential equation must be a polynomial equation in derivatives for the degree to be defined. Therefore, degree of differential equation is 1 .

Find the order and degree of differential equation d 3 y d x 3 + 2 d 2 y d x 2 2 - d y d x + y = 0

Given differential equation is d 3 y d x 3 + 2 d 2 y d x 2 2 - d y d x + y = 0 Here highest order derivative is d 3 y d x 3 and its highest power is 1 . Order: Highest order of derivative occurring in the given differential equation. Therefore, order of differential equation is 3 . Degree: The highest power of the highest order derivative present in the equation and the differential equation must be a polynomial equation in derivatives for the degree to be defined. Therefore, degree of differential equation is 1 .

Find the order and degree of differential equation d 2 y d x 2 3 + d y d x 2 + sin d y d x + 1 = 0

Given differential equation is d 2 y d x 2 3 + d y d x 2 + sin d y d x + 1 = 0 Here highest order derivative is d 2 y d x 2 . Therefore, the order of differential equation is 2 . Differential equation cannot be expressed as polynomial in derivative because sin d y d x is present in the equation. Therefore, its degree is not defined.

Find the order and degree of differential equation d 2 y d x 2 + 3 d y d x = y sin d 2 y d x 2

Given differential equation is d 2 y d x 2 + 3 d y d x = y sin d 2 y d x 2 Here, highest order of derivative is d 2 y d x 2 . Therefore, order of differential equation is 2 . Differential equation cannot be expressed as polynomial in derivative, since it contains the term sin d 2 y d x 2 . Therefore, its degree is not defined.

Find the order and degree of differential equation d 3 y d x 3 - 2 sin d 3 y d x 3 = 0

Given differential equation is d 3 y d x 3 - 2 sin d 3 y d x 3 = 0 The highest order of derivative presents in differential equation is d 3 y d x 3 . Therefore, order of differential equation is 3 . Differential equation cannot be expressed as polynomial in derivative, since it contains the term sin d 3 y d x 3 . Therefore, its degree is not defined.

E M B I B E

Eduwiser's INTEGRAL CALCULUS For JEE Main & Advanced>Chapter 5 - Differential Equations - I>EXERCISE>Q 14

EASY

JEE Main

IMPORTANT

Earn 100

Find the order and degree of differential equation $\frac{d^{3} y}{d x^{3}} + {(\frac{d^{2} y}{d x^{2}})}^{3} + \frac{d y}{d x} + 4 y = \sin x$ . State also whether it is linear or non-linear

Important Questions on Differential Equations - I

EASY

JEE Main

IMPORTANT

Eduwiser's INTEGRAL CALCULUS For JEE Main & Advanced>Chapter 5 - Differential Equations - I>EXERCISE>Q 15

Find the order and degree of differential equation $5 \frac{d^{2} y}{d x^{2}} = {[1 + {(\frac{d y}{d x})}^{2}]}^{\frac{3}{2}}$ . State also whether it is linear or non-linear.