Advertisements
Advertisements
Question
Form a differential equation representing the given family of curves by eliminating arbitrary constants a and b.
`x/a + y/b = 1`
Advertisements
Solution
`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
RELATED QUESTIONS
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.
y2 = a (b2 – x2)
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 = e2x (a + bx)
Solve the differential equation `ye^(x/y) dx = (xe^(x/y) + y^2)dy, (y != 0)`
Find a particular solution of the differential equation (x - y) (dx + dy) = dx - dy, given that y = -1, when x = 0. (Hint: put x - y = t)
The general solution of the differential equation `(y dx - x dy)/y = 0` is ______.
The general solution of a differential equation of the type `dx/dy + P_1 x = Q_1` is ______.
The general solution of the differential equation ex dy + (y ex + 2x) dx = 0 is ______.
Find the differential equation of all the circles which pass through the origin and whose centres lie on x-axis.
Verify that xy = a ex + b e−x + x2 is a solution of the differential equation \[x\frac{d^2 y}{d x^2} + 2\frac{dy}{dx} - xy + x^2 - 2 = 0.\]
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 \[\frac{d^3 y}{d x^3} = 0.\]
From x2 + y2 + 2ax + 2by + c = 0, derive a differential equation not containing a, b and c.
\[\frac{dy}{dx} = \sin^3 x \cos^4 x + x\sqrt{x + 1}\]
\[\frac{dy}{dx} = \frac{1}{x^2 + 4x + 5}\]
\[\frac{dy}{dx} = y^2 + 2y + 2\]
\[\frac{dy}{dx} - x \sin^2 x = \frac{1}{x \log x}\]
\[\frac{dy}{dx} = \sin^3 x \cos^2 x + x e^x\]
(1 + x) y dx + (1 + y) x dy = 0
(1 − x2) dy + xy dx = xy2 dx
A solution of the differential equation `("dy"/"dx")^2 - x "dy"/"dx" + y` = 0 is ______.
General solution of tan 5θ = cot 2θ is
Solution of the equation 3 tan(θ – 15) = tan(θ + 15) is
The number of arbitrary constant in the general solution of a differential equation of fourth order are
The general solution of the differential equation of the type `(dx)/(dy) + p_1y = theta_1` is
Find the general solution of differential equation `(dy)/(dx) = (1 - cosx)/(1 + cosx)`
The general solution of the differential equation y dx – x dy = 0 is ______.
Solve the differential equation: y dx + (x – y2)dy = 0
