Advertisements
Advertisements
प्रश्न
The integrating factor of the differential equation `dy/dx - y = x` is e−x.
विकल्प
True
False
Advertisements
उत्तर
This statement is True.
Explanation:
The given differential equation is:
`dy/dx - y = x`
This is a linear differential equation in the standard form:
`dy/dx + P(x)y = Q(x)`
Here, P(x) = −1, so the integrating factor (IF) is:
IF = `e^(int P(x) dx)`
= `e^(int -1 dx)`
= `e^(-x)`
संबंधित प्रश्न
Form the differential equation of the family of hyperbolas having foci on x-axis and centre at the origin.
Differential equation \[\frac{d^2 y}{d x^2} - y = 0, y \left( 0 \right) = 2, y' \left( 0 \right) = 0\] Function y = ex + e−x
Differential equation \[\frac{d^2 y}{d x^2} - 3\frac{dy}{dx} + 2y = 0, y \left( 0 \right) = 1, y' \left( 0 \right) = 3\] Function y = ex + e2x
tan y \[\frac{dy}{dx}\] = sin (x + y) + sin (x − y)
(y2 + 1) dx − (x2 + 1) dy = 0
Find the particular solution of edy/dx = x + 1, given that y = 3, when x = 0.
Find the particular solution of the differential equation \[\frac{dy}{dx} = - 4x y^2\] given that y = 1, when x = 0.
(x + 2y) dx − (2x − y) dy = 0
Solve the following initial value problem:
\[x\frac{dy}{dx} + y = x \cos x + \sin x, y\left( \frac{\pi}{2} \right) = 1\]
Solve the following initial value problem:
\[\frac{dy}{dx} + y \cot x = 4x\text{ cosec }x, y\left( \frac{\pi}{2} \right) = 0\]
Solve the following initial value problem:-
\[\frac{dy}{dx} + y\cot x = 2\cos x, y\left( \frac{\pi}{2} \right) = 0\]
The rate of increase in the number of bacteria in a certain bacteria culture is proportional to the number present. Given the number triples in 5 hrs, find how many bacteria will be present after 10 hours. Also find the time necessary for the number of bacteria to be 10 times the number of initial present.
Experiments show that radium disintegrates at a rate proportional to the amount of radium present at the moment. Its half-life is 1590 years. What percentage will disappear in one year?
The equation of the curve whose slope is given by \[\frac{dy}{dx} = \frac{2y}{x}; x > 0, y > 0\] and which passes through the point (1, 1) is
Which of the following differential equations has y = C1 ex + C2 e−x as the general solution?
If xmyn = (x + y)m+n, prove that \[\frac{dy}{dx} = \frac{y}{x} .\]
In the following example, verify that the given function is a solution of the corresponding differential equation.
| Solution | D.E. |
| y = xn | `x^2(d^2y)/dx^2 - n xx (xdy)/dx + ny =0` |
Solve the following differential equation.
`(dθ)/dt = − k (θ − θ_0)`
Solve the following differential equation.
`dy /dx +(x-2 y)/ (2x- y)= 0`
Choose the correct alternative.
Bacteria increases at the rate proportional to the number present. If the original number M doubles in 3 hours, then the number of bacteria will be 4M in
Solve the differential equation:
`e^(dy/dx) = x`
Solve:
(x + y) dy = a2 dx
Solve the following differential equation `("d"y)/("d"x)` = x2y + y
Solve: `("d"y)/("d"x) + 2/xy` = x2
The integrating factor of the differential equation `"dy"/"dx" (x log x) + y` = 2logx is ______.
Solve the differential equation `"dy"/"dx"` = 1 + x + y2 + xy2, when y = 0, x = 0.
If `y = log_2 log_2(x)` then `(dy)/(dx)` =
