Advertisements
Advertisements
प्रश्न
Solve the differential equation:
dr = a r dθ − θ dr
उत्तर
dr = a r dθ − θ dr
∴ (1 + θ) dr = a r dθ
∴ `(dr)/r = a (dθ)/((1 + θ))`
Integrating on both sides, we get
`int (dr)/r = a int (dθ)/(1+θ)`
log | r | = a log | 1 + θ| + log | c |
∴ log | r | = log | c(1 + θ)a|
∴ r = c (1 + θ)a
APPEARS IN
संबंधित प्रश्न
Show that y = ax3 + bx2 + c is a solution of the differential equation \[\frac{d^3 y}{d x^3} = 6a\].
For the following differential equation verify that the accompanying function is a solution:
| Differential equation | Function |
|
\[x^3 \frac{d^2 y}{d x^2} = 1\]
|
\[y = ax + b + \frac{1}{2x}\]
|
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
C' (x) = 2 + 0.15 x ; C(0) = 100
\[x^2 \frac{dy}{dx} = x^2 + xy + y^2 \]
Show that the equation of the curve whose slope at any point is equal to y + 2x and which passes through the origin is y + 2 (x + 1) = 2e2x.
Show that all curves for which the slope at any point (x, y) on it is \[\frac{x^2 + y^2}{2xy}\] are rectangular hyperbola.
The differential equation \[x\frac{dy}{dx} - y = x^2\], has the general solution
What is integrating factor of \[\frac{dy}{dx}\] + y sec x = tan x?
Form the differential equation of the family of circles having centre on y-axis and radius 3 unit.
Solve the following differential equation.
`(x + y) dy/dx = 1`
Choose the correct alternative.
The solution of `x dy/dx = y` log y is
`xy dy/dx = x^2 + 2y^2`
Solve `("d"y)/("d"x) = (x + y + 1)/(x + y - 1)` when x = `2/3`, y = `1/3`
For the differential equation, find the particular solution (x – y2x) dx – (y + x2y) dy = 0 when x = 2, y = 0
State whether the following statement is True or False:
The integrating factor of the differential equation `("d"y)/("d"x) - y` = x is e–x
