Advertisements
Advertisements
प्रश्न
Solve the following differential equation.
`dy/dx + y` = 3
Advertisements
उत्तर
`dy/dx + y` = 3
The given equation is of the form
`dy/dx + py = Q`
where, P = 1 and Q = 3
∴ I.F. = `e int^(pdx) = e int^ (1dx) = e^x`
∴ Solution of the given equation is
`y(I.F.) = int Q(I.F.) dx + c`
∴ `ye^x = int 3e^x dx + c`
∴ yex = 3ex + c
संबंधित प्रश्न
For the following differential equation verify that the accompanying function is a solution:
| Differential equation | Function |
|
\[x + y\frac{dy}{dx} = 0\]
|
\[y = \pm \sqrt{a^2 - x^2}\]
|
For the following differential equation verify that the accompanying function is a solution:
| Differential equation | Function |
|
\[x\frac{dy}{dx} + y = y^2\]
|
\[y = \frac{a}{x + a}\]
|
Differential equation \[\frac{d^2 y}{d x^2} - y = 0, y \left( 0 \right) = 2, y' \left( 0 \right) = 0\] Function y = ex + e−x
Find the solution of the differential equation cos y dy + cos x sin y dx = 0 given that y = \[\frac{\pi}{2}\], when x = \[\frac{\pi}{2}\]
The decay rate of radium at any time t is proportional to its mass at that time. Find the time when the mass will be halved of its initial mass.
Find the equation of the curve which passes through the point (1, 2) and the distance between the foot of the ordinate of the point of contact and the point of intersection of the tangent with x-axis is twice the abscissa of the point of contact.
Find the equation of the curve that passes through the point (0, a) and is such that at any point (x, y) on it, the product of its slope and the ordinate is equal to the abscissa.
Integrating factor of the differential equation cos \[x\frac{dy}{dx} + y\] sin x = 1, is
The differential equation satisfied by ax2 + by2 = 1 is
The integrating factor of the differential equation \[x\frac{dy}{dx} - y = 2 x^2\]
Form the differential equation of the family of circles having centre on y-axis and radius 3 unit.
Solve the following differential equation.
`dy /dx +(x-2 y)/ (2x- y)= 0`
Solve the following differential equation.
`dy/dx + y = e ^-x`
Solve the following differential equation.
y dx + (x - y2 ) dy = 0
Solve `("d"y)/("d"x) = (x + y + 1)/(x + y - 1)` when x = `2/3`, y = `1/3`
Solve the following differential equation `("d"y)/("d"x)` = x2y + y
Solve: `("d"y)/("d"x) + 2/xy` = x2
Solve the following differential equation
`x^2 ("d"y)/("d"x)` = x2 + xy − y2
The integrating factor of the differential equation `"dy"/"dx" (x log x) + y` = 2logx is ______.
There are n students in a school. If r % among the students are 12 years or younger, which of the following expressions represents the number of students who are older than 12?
