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
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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:-
\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 = cosx + C : y' + sinx = 0
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