Advertisements
Advertisements
Question
Choose the correct alternative:
General solution of `y - x ("d"y)/("d"x)` = 0 is
Options
`3log x + 7/y` = c
`2log x + 3/y = c`
log x – log y = log c
`3log y + 2/x` = c
Advertisements
Solution
log x – log y = log c
RELATED QUESTIONS
Differential equation \[\frac{dy}{dx} = y, y\left( 0 \right) = 1\]
Function y = ex
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
xy dy = (y − 1) (x + 1) dx
tan y \[\frac{dy}{dx}\] = sin (x + y) + sin (x − y)
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).
\[x^2 \frac{dy}{dx} = x^2 + xy + y^2 \]
3x2 dy = (3xy + y2) dx
Solve the following initial value problem:-
\[\frac{dy}{dx} - 3y \cot x = \sin 2x; y = 2\text{ when }x = \frac{\pi}{2}\]
Solve the following initial value problem:-
\[dy = \cos x\left( 2 - y\text{ cosec }x \right)dx\]
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 the interest is compounded continuously at 6% per annum, how much worth Rs 1000 will be after 10 years? How long will it take to double Rs 1000?
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?
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.
Find the equation of the curve passing through the point (0, 1) if the slope of the tangent to the curve at each of its point is equal to the sum of the abscissa and the product of the abscissa and the ordinate of the point.
Write the differential equation representing the family of straight lines y = Cx + 5, where C is an arbitrary constant.
Integrating factor of the differential equation cos \[x\frac{dy}{dx} + y \sin x = 1\], is
Solve the following differential equation.
y dx + (x - y2 ) dy = 0
The solution of `dy/ dx` = 1 is ______
Select and write the correct alternative from the given option for the question
The differential equation of y = Ae5x + Be–5x is
Solve the following differential equation
`x^2 ("d"y)/("d"x)` = x2 + xy − y2
An appropriate substitution to solve the differential equation `"dx"/"dy" = (x^2 log(x/y) - x^2)/(xy log(x/y))` is ______.
Given that `"dy"/"dx" = "e"^-2x` and y = 0 when x = 5. Find the value of x when y = 3.
The differential equation of all non horizontal lines in a plane is `("d"^2x)/("d"y^2)` = 0
