Class 12 Mathematics - Chapter Differential Equations NCERT Solutions | The degree of the differential equation
The degree of the differential equation
\begin{align}\left(\frac{d^2y}{dx^2}\right)^3\;+ \left(\frac{dy}{dx}\right)^2+\;sin\left(\frac{dy}{dx}\right)\;+ 1=\;0\end{align}
is (A) 3 (B) 2 (C) 1 (D) not defined
\begin{align}\left(\frac{d^2y}{dx^2}\right)^3\;+ \left(\frac{dy}{dx}\right)^2+\;sin\left(\frac{dy}{dx}\right)\;+ 1=\;0\end{align}
The given differential equation is not a polynomial equation in its derivatives. Therefore, its degree is not defined.
Hence, the correct answer is D.
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:- \begin{align} \int \frac{x^3 + 5x^2 - 4}{x^2} . dx\end{align}
- Q:- The volume of a cube is increasing at the rate of 8 cm3/s. How fast is the surface area increasing when the length of an edge is 12 cm?
- Q:- Find the principal value of \begin{align} sec^{-1}\left(\frac{2}{\sqrt3}\right)\end{align}
- Q:-
Consider f : {1, 2, 3} → {a, b, c} given by f(1) = a, f(2) = b and f(3) = c. Find f –1 and show that (f –1)–1 = f.
- Q:- If a matrix has 18 elements, what are the possible orders it can have? What, if it has 5 elements?
- Q:-
The total cost C (x) in Rupees associated with the production of x units of an item is given by
C(X) = 0.007 x3 - 0.003x2 + 15x + 4000
Find the marginal cost when 17 units are produced.
- Q:- \begin{align} \int sec x . \left(sec x + tan x\right) .dx \end{align}
- Q:-
Let f : R → R be defined as f(x) = 3x. Choose the correct answer.
(A) f is one-one onto
(B) f is many-one onto
(C) f is one-one but not onto
(D) f is neither one-one nor onto.
- Q:- The anti derivative of \begin{align} \left(\sqrt x + \frac {1}{\sqrt x}\right)\end{align} equals to \begin{align} (A) \frac{1}{3}.x^\frac{1}{3} + 2.x^\frac{1}{2} +C \;\;\;\; (B) \frac{2}{3}.x^\frac{2}{3} + \frac{1}{2}.x^2 +C \end{align}
\begin{align} (C) \frac{2}{3}.x^\frac{3}{2} +2 x^\frac{1}{2} +C \;\;\;\;(D) \frac{3}{2}.x^\frac{3}{2} +\frac{1}{2}. x^\frac{1}{2} +C \end{align} - Q:-
Represent graphically a displacement of 40 km, 30° east of north.
- All Chapters Of Class 12 Mathematics
- All Subjects Of Class 12