Advertisements
Advertisements
प्रश्न
Find the general solution of the differential equation `"dy"/"dx" = y/x`.
उत्तर
`"dy"/"dx" = y/x`
⇒ `"dy"/y = "dx"/x`
⇒ `int "dy"/y = int "dx"/x`
⇒ logy = logx + logc
⇒ y = cx
APPEARS IN
संबंधित प्रश्न
Find the differential equation of the family of lines passing through the origin.
Find the differential equation representing the family of curves v=A/r+ B, where A and B are arbitrary constants.
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.
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.
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.
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.
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 \[\frac{d^3 y}{d x^3} = 0.\]
\[\frac{dy}{dx} = \sin^3 x \cos^4 x + x\sqrt{x + 1}\]
\[\frac{dy}{dx} - x \sin^2 x = \frac{1}{x \log x}\]
(1 − x2) dy + xy dx = xy2 dx
Solve the differential equation:
cosec3 x dy − cosec y dx = 0
General solution of tan 5θ = cot 2θ is
Solution of the equation 3 tan(θ – 15) = tan(θ + 15) is
Which of the following equations has `y = c_1e^x + c_2e^-x` as the general solution?
The general solution of the differential equation `(dy)/(dx) = e^(x + y)` is
The general solution of the differential equation of the type `(dx)/(dy) + p_1y = theta_1` is
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)
