Advertisements
Advertisements
Question
State whether the following is True or False:
The integrating factor of the differential equation `dy/dx - y = x` is e-x
Options
True
False
Solution
The integrating factor of the differential equation `dy/dx - y = x` is e-x - True
APPEARS IN
RELATED QUESTIONS
For the following differential equation verify that the accompanying function is a solution:
| Differential equation | Function |
|
\[y = \left( \frac{dy}{dx} \right)^2\]
|
\[y = \frac{1}{4} \left( x \pm a \right)^2\]
|
Differential equation \[\frac{d^2 y}{d x^2} - \frac{dy}{dx} = 0, y \left( 0 \right) = 2, y'\left( 0 \right) = 1\]
Function y = ex + 1
Solve the differential equation \[\left( 1 + x^2 \right)\frac{dy}{dx} + \left( 1 + y^2 \right) = 0\], given that y = 1, when x = 0.
(x2 − y2) dx − 2xy dy = 0
3x2 dy = (3xy + y2) dx
Solve the following initial value problem:-
\[\tan x\left( \frac{dy}{dx} \right) = 2x\tan x + x^2 - y; \tan x \neq 0\] given that y = 0 when \[x = \frac{\pi}{2}\]
A curve is such that the length of the perpendicular from the origin on the tangent at any point P of the curve is equal to the abscissa of P. Prove that the differential equation of the curve is \[y^2 - 2xy\frac{dy}{dx} - x^2 = 0\], and hence find the curve.
Write the differential equation obtained eliminating the arbitrary constant C in the equation xy = C2.
Find the solution of the differential equation
\[x\sqrt{1 + y^2}dx + y\sqrt{1 + x^2}dy = 0\]
Form the differential equation representing the family of parabolas having vertex at origin and axis along positive direction of x-axis.
Determine the order and degree of the following differential equations.
| Solution | D.E |
| y = aex + be−x | `(d^2y)/dx^2= 1` |
Choose the correct alternative.
The differential equation of y = `k_1 + k_2/x` is
Solve the differential equation:
dr = a r dθ − θ dr
For the differential equation, find the particular solution
`("d"y)/("d"x)` = (4x +y + 1), when y = 1, x = 0
An appropriate substitution to solve the differential equation `"dx"/"dy" = (x^2 log(x/y) - x^2)/(xy log(x/y))` is ______.
Integrating factor of the differential equation `"dy"/"dx" - y` = cos x is ex.
Solve the differential equation `"dy"/"dx"` = 1 + x + y2 + xy2, when y = 0, x = 0.
