Advertisements
Advertisements
Question
Find the differential equation of the family of lines passing through the origin.
Advertisements
Solution
Consider the equation, y = mx, where m is the parameter.
Thus, the above equation represents the family of lines which pass through the origin.
`y=mx....(1)`
`y/x=m....(2)`
Differentiating the above equation (1) with respect to x,
`y = mx`
`dy/dx=m xx1`
`=>dy/dx=m`
`=>dy/dx=y/x` [because from equation 2]
`=>dy/dx-y/x=0`
Thus we have eliminated the constant, m.
The required differential equation is
`dy/dx-y/x=0`
APPEARS IN
RELATED QUESTIONS
Write the integrating factor of the following differential equation:
(1+y2) dx−(tan−1 y−x) dy=0
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 = ex (a cos x + b sin x)
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)
Find the differential equation representing the family of curves `y = ae^(bx + 5)`. where a and b are arbitrary constants.
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 \[\left( x - 2y \right)\frac{dy}{dx} + 2x + y = 0.\]
Show that the differential equation of all parabolas which have their axes parallel to y-axis is \[\frac{d^3 y}{d x^3} = 0.\]
\[\frac{dy}{dx} = \frac{1}{x^2 + 4x + 5}\]
\[\frac{dy}{dx} + 4x = e^x\]
\[\frac{dy}{dx} = x^2 e^x\]
\[(\tan^2 x + 2\tan x + 5)\frac{dy}{dx} = 2(1+\tan x)\sec^2x\]
tan y dx + tan x dy = 0
x cos2 y dx = y cos2 x dy
(1 − x2) dy + xy dx = xy2 dx
General solution of tan 5θ = cot 2θ 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 of the type `(dx)/(dy) + p_1y = theta_1` is
The general solution of the differential equation `(ydx - xdy)/y` = 0
The general solution of the differential equation y dx – x dy = 0 is ______.
The general solution of the differential equation ydx – xdy = 0; (Given x, y > 0), is of the form
(Where 'c' is an arbitrary positive constant of integration)
