Advertisements
Advertisements
प्रश्न
Solve the following differential equation.
dr + (2r)dθ= 8dθ
Advertisements
उत्तर
dr + (2r)dθ= 8dθ
`(dr)/(dθ)` + 2r = 8
The given equation is of the form
`(dr)/(dθ) + Pr = Q`
where, P = 2 and Q = 8
I.F. = `e ^(int^(P^dθ) = e^(int^(2^dθ) = e^(2θ)`
Solution of the given equation is
`r(I.F.) = int Q (I.F.) dθ + c`
`re^(2θ) = int 8 e^(2θ) dθ + c`
`re^(2θ) = 8 int e^(2θ) dθ + c`
`re ^(2θ) = 8e^(2θ)/2 + c`
`re ^(2θ) = 4e^(2θ) + c`
APPEARS IN
संबंधित प्रश्न
(sin x + cos x) dy + (cos x − sin x) dx = 0
(ey + 1) cos x dx + ey sin x dy = 0
(y + xy) dx + (x − xy2) dy = 0
Find the solution of the differential equation cos y dy + cos x sin y dx = 0 given that y = \[\frac{\pi}{2}\], when x = \[\frac{\pi}{2}\]
(x + y) (dx − dy) = dx + dy
\[x^2 \frac{dy}{dx} = x^2 + xy + y^2 \]
A population grows at the rate of 5% per year. How long does it take for the population to double?
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.
The normal to a given curve at each point (x, y) on the curve passes through the point (3, 0). If the curve contains the point (3, 4), find its equation.
The solution of the differential equation \[\frac{dy}{dx} = \frac{ax + g}{by + f}\] represents a circle when
The solution of the differential equation y1 y3 = y22 is
Form the differential equation representing the family of curves y = a sin (x + b), where a, b are arbitrary constant.
The differential equation `y dy/dx + x = 0` represents family of ______.
Solve the following differential equation.
x2y dx − (x3 + y3) dy = 0
Solve the following differential equation.
(x2 − y2 ) dx + 2xy dy = 0
Solve the differential equation:
`e^(dy/dx) = x`
Solve:
(x + y) dy = a2 dx
An appropriate substitution to solve the differential equation `"dx"/"dy" = (x^2 log(x/y) - x^2)/(xy log(x/y))` is ______.
Given that `"dy"/"dx" = "e"^-2x` and y = 0 when x = 5. Find the value of x when y = 3.
Solve the differential equation `"dy"/"dx" + 2xy` = y
Solve: ydx – xdy = x2ydx.
Solve the differential equation `dy/dx + xy = xy^2` and find the particular solution when y = 4, x = 1.
The value of `dy/dx` if y = |x – 1| + |x – 4| at x = 3 is ______.
