Advertisements
Advertisements
प्रश्न
Find the differential equation of the family of lines passing through the origin.
Advertisements
उत्तर
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
संबंधित प्रश्न
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.
`x/a + y/b = 1`
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 = ex (a cos x + b sin x)
Find the particular solution of the differential equation (1 + e2x) dy + (1 + y2) ex dx = 0, given that y = 1 when x = 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)
Find the differential equation of all the circles which pass through the origin and whose centres lie on y-axis.
Form the differential equation having \[y = \left( \sin^{- 1} x \right)^2 + A \cos^{- 1} x + B\], where A and B are arbitrary constants, as its general solution.
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 y = C x + 2C2 is a solution of the differential equation \[2 \left( \frac{dy}{dx} \right)^2 + x\frac{dy}{dx} - y = 0.\]
Verify that y = A cos x + sin x satisfies the differential equation \[\cos x\frac{dy}{dx} + \left( \sin x \right)y=1.\]
\[\frac{dy}{dx} = \sin^3 x \cos^4 x + x\sqrt{x + 1}\]
\[\frac{dy}{dx} = x^2 e^x\]
\[\frac{dy}{dx} - x \sin^2 x = \frac{1}{x \log x}\]
\[(\tan^2 x + 2\tan x + 5)\frac{dy}{dx} = 2(1+\tan x)\sec^2x\]
\[\frac{dy}{dx} = \sin^3 x \cos^2 x + x e^x\]
tan y dx + tan x dy = 0
x cos2 y dx = y cos2 x dy
The general solution of the differential equation `(dy)/(dx) + x/y` = 0 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 `x^xdy + (ye^x + 2x) dx` = 0
Find the general solution of differential equation `(dy)/(dx) = (1 - cosx)/(1 + cosx)`
Solve the differential equation: y dx + (x – y2)dy = 0
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)
