Advertisements
Advertisements
प्रश्न
Solve the following differential equation.
y dx + (x - y2 ) dy = 0
उत्तर
y dx + (x - y2 ) dy = 0
∴ y dx = (y2 - x) dy
∴ `dx/dy = (y^2 - x) /y= y - x/y `
∴ `dx/dy + x/y = y`
The given equation is of the form
`dx/dy + Px = Q`
where, P = `1/y` and Q = y
∴ I.F. = `e int^ (pdy) = e int ^(1/ydy) = e ^(log |y|)= y`
∴ Solution of the given equation is
`x (I.F.) =int Q (I.F.) dy + c_1`
∴ `xy = int y(y) dy = y^3/3 + c_1`
∴ 3xy = y3 + c …[3c1 = c]
APPEARS IN
संबंधित प्रश्न
(y + xy) dx + (x − xy2) dy = 0
If the marginal cost of manufacturing a certain item is given by C' (x) = \[\frac{dC}{dx}\] = 2 + 0.15 x. Find the total cost function C (x), given that C (0) = 100.
Find the equation to the curve satisfying x (x + 1) \[\frac{dy}{dx} - y\] = x (x + 1) and passing through (1, 0).
Show that y = ae2x + be−x is a solution of the differential equation \[\frac{d^2 y}{d x^2} - \frac{dy}{dx} - 2y = 0\]
Solve the following differential equation.
`(dθ)/dt = − k (θ − θ_0)`
Solve the following differential equation.
`dy /dx +(x-2 y)/ (2x- y)= 0`
Solve the differential equation:
`e^(dy/dx) = x`
y dx – x dy + log x dx = 0
Solve the differential equation sec2y tan x dy + sec2x tan y dx = 0
Integrating factor of the differential equation `"dy"/"dx" - y` = cos x is ex.
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"` = 1 + x + y2 + xy2, when y = 0, x = 0.
The differential equation of all non horizontal lines in a plane is `("d"^2x)/("d"y^2)` = 0
`d/(dx)(tan^-1 (sqrt(1 + x^2) - 1)/x)` is equal to:
