Advertisements
Advertisements
Question
The general solution of the differential equation `(y dx - x dy)/y = 0` is ______.
Options
xy = C
x = Cy2
y = Cx
y = Cx2
Solution
The general solution of the differential equation `(y dx - x dy)/y = 0` is y = Cx.
Explanation:
Given the differential equation
`(y dx - x dy)/y = 0`
or `dx - y/x dy = 0`
and `dx/x - dy/y = 0`
On integrating,
⇒ log |x| - log |y| = log |C'|
⇒ `log |x/y| = log |C'|`
⇒ `x/y = C'`
⇒ `y = 1/C' x`
⇒ y = Cx
Where `1/C = C`
Which is the required solution.
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.
`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 = 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)`
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 a differential equation of the type `dx/dy + P_1 x = Q_1` is ______.
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
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.
\[\frac{dy}{dx} = \sin^3 x \cos^4 x + x\sqrt{x + 1}\]
\[\frac{dy}{dx} = y^2 + 2y + 2\]
\[\frac{dy}{dx} = x^2 e^x\]
\[(\tan^2 x + 2\tan x + 5)\frac{dy}{dx} = 2(1+\tan x)\sec^2x\]
tan y dx + tan x dy = 0
cos y log (sec x + tan x) dx = cos x log (sec y + tan y) dy
(1 − x2) dy + xy dx = xy2 dx
Find the general solution of the differential equation `"dy"/"dx" = y/x`.
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
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)`
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 ______.
Solve the differential equation: y dx + (x – y2)dy = 0
