Determine order and degree(if defined) of differential equation yn + (y')2 + 2y =0
yn + (y')2 + 2y =0
The highest order derivative present in the differential equation is yn. Therefore, its order is two.
The given differential equation is a polynomial equation in yn and y' and the highest power raised to yn is one.
Hence, its degree is one.
Determine order and degree(if defined) of differential equation y' + 5y = 0
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}
Determine order and degree(if defined) of differential equation (ym)2 + (yn)3 + (y')4 + y5 =0
Determine order and degree(if defined) of differential equation yn + 2y' + siny = 0
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
Determine order and degree(if defined) of differential y' + y =ex
y = Ax : xy' = y (x ≠ 0)
\begin{align} y = xsinx:xy{'}=y +x\sqrt{x^2 -y^2}(x\neq0\; and\; x>y\; or\; x<-y)\end{align}
Determine order and degree(if defined) of differential equation ym + 2yn + y' =0
y = cosx + C : y' + sinx = 0
Prove that the function f(x) = 5x – 3 is continuous at x = 0, at x = – 3 and at x = 5.
Represent graphically a displacement of 40 km, 30° east of north.
If a line makes angles 90°, 135°, 45° with x, y and z-axes respectively, find its direction cosines.
Maximise Z = 3x + 4y
Subject to the constraints:x + y ≤ 4, x ≥ 0, y ≥ 0
Find the area of the region bounded by the curve y2 = x and the lines x = 1, x = 4 and the x-axis.
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).
A particle moves along the curve 6y = x3 + 2. Find the points on the curve at which the y-coordinate is changing 8 times as fast as the x-coordinate.
If f(x) = , show that fof(x) = x, for all x ≠ 2/3. What is the inverse of f ?
Consider f : R → R given by f(x) = 4x + 3. Show that f is invertible. Find the inverse of f.
Find the area of the region bounded by the curve y2 = x and the lines x = 1, x = 4 and the x-axis.
Let f: X → Y be an invertible function. Show that the inverse of f –1 is f, i.e., (f–1)–1 = f.
Consider f : R+ → [4, ∞) given by f(x) = x2 + 4. Show that f is invertible with the inverse f–1 of f given by , where R+ is the set of all non-negative real numbers.