Advertisements
Advertisements
Question
What is integrating factor of \[\frac{dy}{dx}\] + y sec x = tan x?
Options
sec x + tan x
log (sec x + tan x)
esec x
sec x
Advertisements
Solution
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
RELATED QUESTIONS
Prove that:
`int_0^(2a)f(x)dx = int_0^af(x)dx + int_0^af(2a - x)dx`
Verify that y2 = 4ax is a solution of the differential equation y = x \[\frac{dy}{dx} + a\frac{dx}{dy}\]
Verify that y = − x − 1 is a solution of the differential equation (y − x) dy − (y2 − x2) dx = 0.
Differential equation \[x\frac{dy}{dx} = 1, y\left( 1 \right) = 0\]
Function y = log x
x cos2 y dx = y cos2 x dy
Solve the differential equation \[x\frac{dy}{dx} + \cot y = 0\] given that \[y = \frac{\pi}{4}\], when \[x=\sqrt{2}\]
The volume of a spherical balloon being inflated changes at a constant rate. If initially its radius is 3 units and after 3 seconds it is 6 units. Find the radius of the balloon after `t` seconds.
The rate of growth of a population is proportional to the number present. If the population of a city doubled in the past 25 years, and the present population is 100000, when will the city have a population of 500000?
If sin x is an integrating factor of the differential equation \[\frac{dy}{dx} + Py = Q\], then write the value of P.
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
Find the coordinates of the centre, foci and equation of directrix of the hyperbola x2 – 3y2 – 4x = 8.
For each of the following differential equations find the particular solution.
(x − y2 x) dx − (y + x2 y) dy = 0, when x = 2, y = 0
Solve the following differential equation.
`xy dy/dx = x^2 + 2y^2`
Solve the following differential equation.
y dx + (x - y2 ) dy = 0
The solution of `dy/dx + x^2/y^2 = 0` is ______
Choose the correct alternative.
The solution of `x dy/dx = y` log y is
Solve:
(x + y) dy = a2 dx
`dy/dx = log x`
Solve `("d"y)/("d"x) = (x + y + 1)/(x + y - 1)` when x = `2/3`, y = `1/3`
Solve the differential equation xdx + 2ydy = 0
Solve the following differential equation y2dx + (xy + x2) dy = 0
A solution of differential equation which can be obtained from the general solution by giving particular values to the arbitrary constant is called ______ solution
Verify y = `a + b/x` is solution of `x(d^2y)/(dx^2) + 2 (dy)/(dx)` = 0
y = `a + b/x`
`(dy)/(dx) = square`
`(d^2y)/(dx^2) = square`
Consider `x(d^2y)/(dx^2) + 2(dy)/(dx)`
= `x square + 2 square`
= `square`
Hence y = `a + b/x` is solution of `square`
Solve the differential equation `"dy"/"dx" + 2xy` = y
The differential equation of all non horizontal lines in a plane is `("d"^2x)/("d"y^2)` = 0
If `y = log_2 log_2(x)` then `(dy)/(dx)` =
Solve the differential equation
`y (dy)/(dx) + x` = 0
