Advertisements
Advertisements
प्रश्न
Select and write the correct alternative from the given option for the question
Differential equation of the function c + 4yx = 0 is
पर्याय
`xy + ("d"y)/("d"x)` = 0
`x ("d"y)/("d"x) + y` = 0
`("d"y)/("d"x) - 4xy` = 0
`x ("d"y)/("d"x) + 1` = 0
Advertisements
उत्तर
`x ("d"y)/("d"x) + y` = 0
संबंधित प्रश्न
Solve the equation for x: `sin^(-1) 5/x + sin^(-1) 12/x = π/2, x ≠ 0`
Form the differential equation of the family of hyperbolas having foci on x-axis and centre at the origin.
Verify that y = 4 sin 3x is a solution of the differential equation \[\frac{d^2 y}{d x^2} + 9y = 0\]
Verify that \[y = e^{m \cos^{- 1} x}\] satisfies the differential equation \[\left( 1 - x^2 \right)\frac{d^2 y}{d x^2} - x\frac{dy}{dx} - m^2 y = 0\]
Differential equation \[\frac{d^2 y}{d x^2} + y = 0, y \left( 0 \right) = 0, y' \left( 0 \right) = 1\] Function y = sin x
C' (x) = 2 + 0.15 x ; C(0) = 100
(y + xy) dx + (x − xy2) dy = 0
(y2 + 1) dx − (x2 + 1) dy = 0
dy + (x + 1) (y + 1) dx = 0
2xy dx + (x2 + 2y2) dy = 0
Solve the following initial value problem:-
\[y' + y = e^x , y\left( 0 \right) = \frac{1}{2}\]
Solve the following initial value problem:-
\[\frac{dy}{dx} + 2y = e^{- 2x} \sin x, y\left( 0 \right) = 0\]
Solve the following initial value problem:-
\[\frac{dy}{dx} + y \tan x = 2x + x^2 \tan x, y\left( 0 \right) = 1\]
Solve the following initial value problem:-
\[\frac{dy}{dx} + 2y \tan x = \sin x; y = 0\text{ when }x = \frac{\pi}{3}\]
The surface area of a balloon being inflated, changes at a rate proportional to time t. If initially its radius is 1 unit and after 3 seconds it is 2 units, find the radius after time t.
In a culture, the bacteria count is 100000. The number is increased by 10% in 2 hours. In how many hours will the count reach 200000, if the rate of growth of bacteria is proportional to the number present?
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.
The differential equation satisfied by ax2 + by2 = 1 is
The differential equation \[x\frac{dy}{dx} - y = x^2\], has the general solution
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 \[\frac{dy}{dx} = \frac{y}{x} .\]
y2 dx + (x2 − xy + y2) dy = 0
Verify that the function y = e−3x is a solution of the differential equation \[\frac{d^2 y}{d x^2} + \frac{dy}{dx} - 6y = 0.\]
Solve the differential equation:
`"x"("dy")/("dx")+"y"=3"x"^2-2`
The differential equation `y dy/dx + x = 0` represents family of ______.
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` |
Solve the following differential equation.
`y^3 - dy/dx = x dy/dx`
Solve the following differential equation.
`(x + a) dy/dx = – y + a`
y2 dx + (xy + x2)dy = 0
x2y dx – (x3 + y3) dy = 0
Solve the differential equation xdx + 2ydy = 0
Given that `"dy"/"dx"` = yex and x = 0, y = e. Find the value of y when x = 1.
Solve: ydx – xdy = x2ydx.
Why is the equation \[x\frac{dy}{dx} + y = 0\] classified as a differential equation?
