Class 12 Mathematics - Chapter Differential Equations NCERT Solutions | Determine order and degree(if defined) o
Determine order and degree(if defined) of differential equation \begin{align} \frac{d^4y}{dx^4}\;+\;\sin(y^m)\;=0\end{align}
\begin{align} \frac{d^4y}{dx^4}\;+\;\sin(y^m)\;=0 \end{align}
\begin{align} \Rightarrow y^{m\;'}+\;\sin(y^m)\;=0 \end{align}
The highest order derivative present in the differential equation is ym '. Therefore, its order is four.
The given differential equation is not a polynomial equation in its derivatives. Hence, its degree is not defined.
More Questions From Class 12 Mathematics - Chapter Differential Equations
- 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 (ym)2 + (yn)3 + (y')4 + y5 =0
- Q:-
Determine order and degree(if defined) of differential equation yn + 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 =ex
- 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 ym + 2yn + y' =0
- Q:-
Determine order and degree(if defined) of differential equation yn + (y')2 + 2y =0
Popular Questions of Class 12 Mathematics
- 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 = 3x + 4y
Subject to the constraints:x + y ≤ 4, x ≥ 0, y ≥ 0
- Q:-
Find the area of the region bounded by the curve y2 = 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
Recently Viewed Questions of Class 12 Mathematics
- Q:-
Find the direction cosines of a line which makes equal angles with the coordinate axes.
- Q:- If A = \(\begin{bmatrix}1 & 1 & -2\\2 & 1 & -3\\5 & 4 & -9\end{bmatrix}\), Find |A|
- Q:-
Let A and B be sets. Show that f : A × B → B × A such that f(a, b) = (b, a) is bijective function.
- 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:-
Prove that the Greatest Integer Function f : R → R, given by f(x) = [x], is neither one-one nor onto, where [x] denotes the greatest integer less than or equal to x.
- Q:-
Let A = {1, 2, 3}, B = {4, 5, 6, 7} and let f = {(1, 4), (2, 5), (3, 6)} be a function from A to B. Show that f is one-one.
- Q:-
The rate of change of the area of a circle with respect to its radius r at r = 6 cm is
(A) 10π (B) 12π (C) 8π (D) 11π
- Q:- If A=\(\begin{bmatrix}1 & 2\\4 & 2\end{bmatrix}\), then show that |2A| = 4|A|
- Q:-
Let A = R – {3} and B = R – {1}. Consider the function f : A → B defined by
. Is f one-one and onto? Justify your answer. - Q:- Find the value of if \begin{align} sin^{-1} x= y,\end{align}
then
\begin{align} (A) 0 ≤ y ≤ x \;\;\;\;\; (B) -\frac{\pi}{2} ≤ y ≤ \frac{\pi}{2} \end{align}
\begin{align} (C)\; 0 < y < \pi \;\;\;\;\; (D) -\frac{\pi}{2} < y < \frac{\pi}{2} \end{align}
- All Chapters Of Class 12 Mathematics
- All Subjects Of Class 12