Advertisements
Advertisements
प्रश्न
Choose the correct alternative.
The integrating factor of `dy/dx - y = e^x `is ex, then its solution is
पर्याय
ye −x = x + c
yex = x + c
yex = 2x + c
ye−x = 2x + c
Advertisements
उत्तर
The integrating factor of `dy/dx -y = e^x `is ex, then its solution is ye −x = x + c
Explanation
`dy/dx -y = e^x`
Here, I.F. = e–x , Q = ex
∴ Solution of the given equation is
`y ( I.F.) = int Q ( I.F.) dx + c`
∴ `ye ^-x = int e^xe^-x dx+c`
∴ `ye ^-x = int 1dx + c`
∴ ye –x = x + c
APPEARS IN
संबंधित प्रश्न
Solve the equation for x: `sin^(-1) 5/x + sin^(-1) 12/x = π/2, x ≠ 0`
Verify that y = 4 sin 3x is a solution of the differential equation \[\frac{d^2 y}{d x^2} + 9y = 0\]
Differential equation \[\frac{d^2 y}{d x^2} - \frac{dy}{dx} = 0, y \left( 0 \right) = 2, y'\left( 0 \right) = 1\]
Function y = ex + 1
Differential equation \[\frac{d^2 y}{d x^2} + y = 0, y \left( 0 \right) = 1, y' \left( 0 \right) = 1\] Function y = sin x + cos x
(sin x + cos x) dy + (cos x − sin x) dx = 0
Solve the following differential equation:
(xy2 + 2x) dx + (x2 y + 2y) dy = 0
Find the particular solution of the differential equation
(1 – y2) (1 + log x) dx + 2xy dy = 0, given that y = 0 when x = 1.
x2 dy + y (x + y) dx = 0
\[\frac{dy}{dx} = \frac{y}{x} + \sin\left( \frac{y}{x} \right)\]
Find the equation of the curve passing through the point \[\left( 1, \frac{\pi}{4} \right)\] and tangent at any point of which makes an angle tan−1 \[\left( \frac{y}{x} - \cos^2 \frac{y}{x} \right)\] with x-axis.
The normal to a given curve at each point (x, y) on the curve passes through the point (3, 0). If the curve contains the point (3, 4), find its equation.
The slope of a curve at each of its points is equal to the square of the abscissa of the point. Find the particular curve through the point (−1, 1).
If sin x is an integrating factor of the differential equation \[\frac{dy}{dx} + Py = Q\], then write the value of P.
Which of the following transformations reduce the differential equation \[\frac{dz}{dx} + \frac{z}{x}\log z = \frac{z}{x^2} \left( \log z \right)^2\] into the form \[\frac{du}{dx} + P\left( x \right) u = Q\left( x \right)\]
In each of the following examples, verify that the given function is a solution of the corresponding differential equation.
| Solution | D.E. |
| y = ex | `dy/ dx= y` |
For the following differential equation find the particular solution.
`dy/ dx = (4x + y + 1),
when y = 1, x = 0
Solve the following differential equation.
`dy/dx + y = e ^-x`
Solve the following differential equation.
`(x + a) dy/dx = – y + a`
Solve
`dy/dx + 2/ x y = x^2`
Solve the differential equation (x2 – yx2)dy + (y2 + xy2)dx = 0
Choose the correct alternative:
Differential equation of the function c + 4yx = 0 is
The integrating factor of the differential equation `"dy"/"dx" (x log x) + y` = 2logx is ______.
The differential equation of all non horizontal lines in a plane is `("d"^2x)/("d"y^2)` = 0
Solve the differential equation
`x + y dy/dx` = x2 + y2
