Advertisements
Advertisements
Question
Advertisements
Solution
\[s^2 \frac{d^2 t}{d s^2} + st\frac{dt}{ds} = s\]
\[ \Rightarrow s\frac{d^2 t}{d s^2} + t\frac{dt}{ds} = 1\]
In this differential equation, the order of the highest order derivative is 2 and its power is 1. So, it is a differential equation of order 2 and degree 1.
It is a non-linear differential equation, as it contains the product of the dependent variable \[\left( t \right)\] and its differential co-efficient \[\left( \frac{dt}{ds} \right)\].
APPEARS IN
RELATED QUESTIONS
Write the degree of the differential equation `x^3((d^2y)/(dx^2))^2+x(dy/dx)^4=0`
Determine the order and degree (if defined) of the differential equation:
`(d^4y)/(dx^4) + sin(y^("')) = 0`
Determine the order and degree (if defined) of the differential equation:
`(d^2y)/(dx^2)^2 + cos(dy/dx) = 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′ + 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`
Write the order of the differential equation
\[1 + \left( \frac{dy}{dx} \right)^2 = 7 \left( \frac{d^2 y}{d x^2} \right)^3\]
Write the degree of the differential equation
\[\frac{d^2 y}{d x^2} + x \left( \frac{dy}{dx} \right)^2 = 2 x^2 \log \left( \frac{d^2 y}{d x^2} \right)\]
Write the degree of the differential equation x \[\left( \frac{d^2 y}{d x^2} \right)^3 + y \left( \frac{dy}{dx} \right)^4 + x^3 = 0\]
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:-
\[\left( \frac{ds}{dt} \right)^4 + 3s\frac{d^2 s}{d t^2} = 0\]
Determine the order and degree (if defined) of the following differential equation:-
(y"')2 + (y")3 + (y')4 + y5 = 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
In the following verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation:-
y = x sin x `xy'=y+xsqrt(x^2-y^2)`
Find the order and the degree of the differential equation `x^2 (d^2y)/(dx^2) = { 1 + (dy/dx)^2}^4`
Determine the order and degree of the following differential equation:
`("d"^2"y")/"dx"^2 + "x"("dy"/"dx")` + y = 2 sin x
Determine the order and degree of the following differential equation:
`("d"^2"y")/"dx"^2 + 5 "dy"/"dx" + "y" = "x"^3`
Determine the order and degree of the following differential equations.
`(d^4y)/dx^4 + [1+(dy/dx)^2]^3 = 0`
Determine the order and degree of the following differential equations.
`sqrt(1+1/(dy/dx)^2) = (dy/dx)^(3/2)`
Determine the order and degree of the following differential equations.
`dy/dx = 7 (d^2y)/dx^2`
Choose the correct alternative.
The order and degree of `[ 1+ (dy/dx)^3]^(2/3) = 8 (d^3y)/dx^3` are respectively.
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.
Find the order and degree of the following differential equation:
`x+ dy/dx = 1 + (dy/dx)^2`
The power of highest ordered derivative when all the derivatives are made free from negative and/or fractional indices if any is called ______ of the differential equation
State whether the following statement is True or False:
Order and degree of differential equation `x ("d"^3y)/("d"x^3) + 6(("d"^2y)/("d"x^2))^2 + y` = 0 is (2, 2)
The degree of the differential equation `("d"^4"y")/"dx"^4 + sqrt(1 + ("dy"/"dx")^4)` = 0 is
The degree of the differential equation `1/2 ("d"^3"y")/"dx"^3 = {1 + (("d"^2"y")/"dx"^2)}^(5/3)` is ______.
If m and n are the order and degree of the differential equation `((d^3y)/(dx^3))^6+5((d^3y)/(dx^3))^4/((d^4y)/(dx^4))+(d^4y)/(dx^4)=x^3-1,` then ______.
The degree of the differential equation `(1 + "dy"/"dx")^3 = (("d"^2y)/("d"x^2))^2` is ______.
The degree of the differential equation `("d"^2y)/("d"x^2) + 3("dy"/"dx")^2 = x^2 log(("d"^2y)/("d"x^2))` is ______.
The degree of the differential equation `(("d"^2y)/("d"x^2))^2 + (("d"y)/("d"x))^2 = xsin(("d"y)/("d"x))` is ______.
The order and degree of the differential equation `("d"^2y)/("d"x^2) + (("d"y)/("d"x))^(1/4) + x^(1/5)` = 0, respectively, are ______.
Write the sum of the order and the degree of the following differential equation:
`d/(dx) (dy/dx)` = 5
The differential equation representing the family of curves y2 = `2c(x + sqrt(c))`, where c is a positive parameter, is of ______.
Degree of the differential equation `sinx + cos(dy/dx)` = y2 is ______.
The sum of the order and the degree of the differential equation `d/dx[(dy/dx)^3]` is ______.
The degree of the differential equation `[1 + (dy/dx)^2]^3 = ((d^2y)/(dx^2))^2` is ______.
Find the order and degree of the differential equation `(1 + 3 dy/dx)^(2/3) = 4((d^3y)/(dx^3))`.
