Advertisements
Advertisements
प्रश्न
Form a differential equation representing the given family of curves by eliminating arbitrary constants a and b.
`x/a + y/b = 1`
Advertisements
उत्तर
`x/a + y/b = 1`
Differentiating both sides of the given equation with respect to x, we get:

Hence, the required differential equation of the given curve is y" = 0
APPEARS IN
संबंधित प्रश्न
Write the integrating factor of the following differential equation:
(1+y2) dx−(tan−1 y−x) dy=0
Find the differential equation of the family of lines passing through the origin.
Form a differential equation representing the given family of curves by eliminating arbitrary constants a and b.
y = a e3x + b e– 2x
Form a differential equation representing the given family of curves by eliminating arbitrary constants a and b.
y = ex (a cos x + b sin x)
Solve the differential equation `ye^(x/y) dx = (xe^(x/y) + y^2)dy, (y != 0)`
The general solution of the differential equation `(y dx - x dy)/y = 0` is ______.
The general solution of the differential equation ex dy + (y ex + 2x) dx = 0 is ______.
Find the differential equation representing the family of curves `y = ae^(bx + 5)`. where a and b are arbitrary constants.
Find the differential equation of all the circles which pass through the origin and whose centres lie on y-axis.
The equation of the curve satisfying the differential equation y (x + y3) dx = x (y3 − x) dy and passing through the point (1, 1) is
Show that y2 − x2 − xy = a is a solution of the differential equation \[\left( x - 2y \right)\frac{dy}{dx} + 2x + y = 0.\]
Verify that y = A cos x + sin x satisfies the differential equation \[\cos x\frac{dy}{dx} + \left( \sin x \right)y=1.\]
Find the differential equation corresponding to y = ae2x + be−3x + cex where a, b, c are arbitrary constants.
Show that the differential equation of all parabolas which have their axes parallel to y-axis is \[\frac{d^3 y}{d x^3} = 0.\]
\[\frac{dy}{dx} = \sin^3 x \cos^4 x + x\sqrt{x + 1}\]
\[\frac{dy}{dx} = \frac{1}{x^2 + 4x + 5}\]
\[\frac{dy}{dx} = y^2 + 2y + 2\]
\[\frac{dy}{dx} + 4x = e^x\]
\[\frac{dy}{dx} - x \sin^2 x = \frac{1}{x \log x}\]
(1 + x) y dx + (1 + y) x dy = 0
x cos2 y dx = y cos2 x dy
cos y log (sec x + tan x) dx = cos x log (sec y + tan y) dy
cosec x (log y) dy + x2y dx = 0
Solve the differential equation:
cosec3 x dy − cosec y dx = 0
If n is any integer, then the general solution of the equation `cos x - sin x = 1/sqrt(2)` is
The number of arbitrary constant in the general solution of a differential equation of fourth order are
Which of the following equations has `y = c_1e^x + c_2e^-x` as the general solution?
The general solution of the differential equation `(ydx - xdy)/y` = 0
The general solution of the differential equation `x^xdy + (ye^x + 2x) dx` = 0
Find the general solution of differential equation `(dy)/(dx) = (1 - cosx)/(1 + cosx)`
What is the general solution of differential equation `(dy)/(dx) = sqrt(4 - y^2) (-2 < y < 2)`
The general solution of the differential equation y dx – x dy = 0 is ______.
