Advertisements
Advertisements
प्रश्न
What is integrating factor of \[\frac{dy}{dx}\] + y sec x = tan x?
विकल्प
sec x + tan x
log (sec x + tan x)
esec x
sec x
Advertisements
उत्तर
sec x + tan x
We have,
\[\frac{dy}{dx} + y \sec x = \tan x\]
\[\text{ Comparing with }\frac{dy}{dx} + Py = Q, \text{ we get }\]
\[P = \sec x \]
\[Q = \tan x\]
Now,
\[I . F . = e^{\int\sec xdx} \]
\[ = e^{log\left( \sec x + \tan x \right)} \]
\[ = \sec x + \tan x\]
APPEARS IN
संबंधित प्रश्न
Show that the differential equation of which y = 2(x2 − 1) + \[c e^{- x^2}\] is a solution, is \[\frac{dy}{dx} + 2xy = 4 x^3\]
For the following differential equation verify that the accompanying function is a solution:
| Differential equation | Function |
|
\[x^3 \frac{d^2 y}{d x^2} = 1\]
|
\[y = ax + b + \frac{1}{2x}\]
|
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
C' (x) = 2 + 0.15 x ; C(0) = 100
xy (y + 1) dy = (x2 + 1) dx
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.
If y(x) is a solution of the different equation \[\left( \frac{2 + \sin x}{1 + y} \right)\frac{dy}{dx} = - \cos x\] and y(0) = 1, then find the value of y(π/2).
Find the particular solution of the differential equation
(1 – y2) (1 + log x) dx + 2xy dy = 0, given that y = 0 when x = 1.
(y2 − 2xy) dx = (x2 − 2xy) dy
Solve the following differential equations:
\[\frac{dy}{dx} = \frac{y}{x}\left\{ \log y - \log x + 1 \right\}\]
Solve the following initial value problem:-
\[\frac{dy}{dx} + 2y \tan x = \sin x; y = 0\text{ when }x = \frac{\pi}{3}\]
A bank pays interest by continuous compounding, that is, by treating the interest rate as the instantaneous rate of change of principal. Suppose in an account interest accrues at 8% per year, compounded continuously. Calculate the percentage increase in such an account over one year.
The decay rate of radium at any time t is proportional to its mass at that time. Find the time when the mass will be halved of its initial mass.
The slope of the tangent at a point P (x, y) on a curve is \[\frac{- x}{y}\]. If the curve passes through the point (3, −4), find the equation of the curve.
Show that all curves for which the slope at any point (x, y) on it is \[\frac{x^2 + y^2}{2xy}\] are rectangular hyperbola.
Write the differential equation obtained eliminating the arbitrary constant C in the equation xy = C2.
In the following verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation:-
`y=sqrt(a^2-x^2)` `x+y(dy/dx)=0`
Solve the following differential equation.
`dy/dx = x^2 y + y`
Solve the following differential equation.
xdx + 2y dx = 0
The solution of `dy/ dx` = 1 is ______.
y2 dx + (xy + x2)dy = 0
Select and write the correct alternative from the given option for the question
Differential equation of the function c + 4yx = 0 is
Solve the differential equation sec2y tan x dy + sec2x tan y dx = 0
For the differential equation, find the particular solution
`("d"y)/("d"x)` = (4x +y + 1), when y = 1, x = 0
An appropriate substitution to solve the differential equation `"dx"/"dy" = (x^2 log(x/y) - x^2)/(xy log(x/y))` is ______.
Solve the differential equation `"dy"/"dx" + 2xy` = y
