Class 12 Mathematics - Chapter Differential Equations NCERT Solutions | y = Ax : xy' = y (x ≠ 0)
y = Ax : xy' = y (x ≠ 0)
y = Ax
Differentiating both sides with respect to x, we get:
\begin{align}y^{'}=\frac{d}{dx}(Ax)\end{align}
⇒ y ' = A
Substituting the value of y' in the given differential equation, we get:
L.H.S. = xy' = xA = Ax = y = R.H.S.
Hence, the given function is the solution of the corresponding differential equation.
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:-
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 equation yn + 2y' + siny = 0
- Q:-
Determine order and degree(if defined) of differential y' + y =ex
- 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
- Q:-
y = x2 + 2x + C : y' - 2x - 2 = 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.
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- Q:-
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(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
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