This page offers a step-by-step solution to the specific question **NCERT Class 12th Mathematics - Differential Equations | determine order and degree if defined of differen Answer ** from NCERT Class 12th Mathematics, Chapter Differential Equations.

Question 6

Determine order and degree(if defined) of differential equation (y^{m})^{2} + (y^{n})^{3} + (y')^{4} + y^{5} =0

Answer

(y^{m})^{2} + (y^{n})^{3} + (y')^{4} + y^{5} =0

The highest order derivative present in the differential equation isy^{m}. Therefore, its order is three.

The given differential equation is a polynomial equation in y^{m , }y^{n , y'.}

The highest power raised to y^{m }is 2. Hence, its degree is 2.

- Q:-
Determine order and degree(if defined) of differential equation y' + 5y = 0

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

\begin{align}\left(\frac{d^2y}{dx^2}\right)^2\;+\;cos\left(\frac{dy}{dx}\right)\;=\;0\end{align}

- Q:-
Determine order and degree(if defined) of differential equation y

^{n}+ 2y^{'}+ siny = 0 - Q:-
The order of the differential equation

\begin{align}2x^2\frac{d^2y}{dx^2}\;- \;3\frac{dy}{dx}\;+ y=\;0\end{align}

is

**(A)**2**(B)**1**(C)**0**(D)**not defined - Q:-
Determine order and degree(if defined) of differential y

^{'}+ y =e^{x} - Q:-
y = Ax : xy

^{'}= y (x ≠ 0) - Q:-
\begin{align} y = xsinx:xy{'}=y +x\sqrt{x^2 -y^2}(x\neq0\; and\; x>y\; or\; x<-y)\end{align}

- Q:-
Determine order and degree(if defined) of differential equation y

^{m}+ 2y^{n}+ y' =0 - Q:-
y = cosx + C

**:**y^{'}+ sinx = 0 - Q:-
y = e

^{x}+1**:**y^{n}-y^{'}= 0

- Q:-
Prove that the function f(x) = 5x – 3 is continuous at x = 0, at x = – 3 and at x = 5.

- Q:-
Represent graphically a displacement of 40 km, 30° east of north.

- Q:-
If a line makes angles 90°, 135°, 45° with

*x*,*y*and*z*-axes respectively, find its direction cosines. - Q:-
Maximise Z = 3

*x*+ 4*y*Subject to the constraints:

*x*+*y*≤ 4,*x*≥ 0,*y*≥ 0 - Q:-
Find the area of the region bounded by the curve

*y*^{2}=*x*and the lines*x*= 1,*x*= 4 and the*x*-axis. - Q:- Evaluate the determinants

\begin{vmatrix} \mathbf{2} & \mathbf{4} \\ \mathbf{-5} & \mathbf{-1} \end{vmatrix} - Q:- Determine whether each of the following relations are reflexive, symmetric and transitive:

(i) Relation R in the set A = {1, 2, 3,13, 14} defined as

R = {(x, y): 3x − y = 0}

(ii) Relation R in the set N of natural numbers defined as

R = {(x, y): y = x + 5 and x < 4}

(iii) Relation R in the set A = {1, 2, 3, 4, 5, 6} as

R = {(x, y): y is divisible by x}

(iv) Relation R in the set Z of all integers defined as

R = {(x, y): x − y is as integer}

(v) Relation R in the set A of human beings in a town at a particular time given by

(a) R = {(x, y): x and y work at the same place}

(b) R = {(x, y): x and y live in the same locality}

(c) R = {(x, y): x is exactly 7 cm taller than y}

(d) R = {(x, y): x is wife of y}

(e) R = {(x, y): x is father of y} - Q:- Find the rate of change of the area of a circle with respect to its radius r when

(a) r = 3 cm

(b) r = 4 cm - Q:-
Given that E and F are events such that P(E) = 0.6, P(F) = 0.3 and P(E ∩ F) = 0.2, find P (E|F) and P(F|E).

- Q:- Integrals sin 2x

- Q:- Given an example of a relation. Which is

(i) Symmetric but neither reflexive nor transitive.

(ii) Transitive but neither reflexive nor symmetric.

(iii) Reflexive and symmetric but not transitive.

(iv) Reflexive and transitive but not symmetric.

(v) Symmetric and transitive but not reflexive. - Q:-
The total revenue in Rupees received from the sale of

*x*units of a product is given byR (x) = 13x

^{2}+ 26x + 15Find the marginal revenue when

*x*= 7. - Q:-
An edge of a variable cube is increasing at the rate of 3 cm/s. How fast is the volume of the cube increasing when the edge is 10 cm long?

- Q:-
A balloon, which always remains spherical on inflation, is being inflated by pumping in 900 cubic centimetres of gas per second. Find the rate at which the radius of the balloon increases when the radius is 15 cm.

- Q:- Show that each of the relation R in the set A = { x ∈Z: 0≤x≤12}, A={x} given by

(i) R = { (a,b) : |a - b| is a multiple of 4}

(ii) R = {(a,b):a = b} is an equivalence relation.

Find the set of all elements related to 1 in each case. - Q:- Show that the relation R in the set {1, 2, 3} given by R = {(1, 2), (2, 1)} is symmetric but neither reflexive nor transitive.
- Q:-
In each of the following cases, state whether the function is one-one, onto or bijective. Justify your answer.

(i)

*f*:**R → R**defined by*f(x)*= 3 – 4x(ii)

*f*:**R → R**defined by*f(x)*= 1 + x^{2 } - Q:- Show that the relation R in the set A of all the books in a library of a college, given by R = {(x, y): x and y have same number of pages} is an equivalence relation.
- Q:- \begin{align} \int sec x . \left(sec x + tan x\right) .dx \end{align}
- Q:-
Show that the function

*f*: R_{*}→ R_{*}defined by*f(x)*= 1/x is one-one and onto,where R_{*}is the set of all non-zero real numbers. Is the result true, if the domain R_{*}is replaced by N with co-domain being same as R_{* }?

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