Advertisements
Advertisements
प्रश्न
Solve : cos x(1 + cosy) dx – sin y(1 + sinx) dy = 0
Advertisements
उत्तर
cos x(1 + cos y) dx = sin y(1 + sin x) dy
`cosx/((1 + sin x)) "d"x = siny/((1 + cos y)) "d"y`
Integrating on both sides
`int cosx/((1 + sin x)) "d"x = int siny/((1 + cos y)) "d"y`
`int cosx/((1 + sin x)) "d"x = - int (-siny)/((1 + cos y)) "d"y`
`log (1 + sin x) = - log (1 + cos y) + log "c"`
`log(1 + sin x) = log ("c"/((1 + cos y)))`
`(1 + sin x) = "c"/((1 + cos y))`
⇒ (1 + sin x)(1 + cos y) = c
APPEARS IN
संबंधित प्रश्न
Solve the following differential equation:
`("d"y)/("d"x) = "e"^(x + y) - x^3"e"^y`
Solve the following differential equation:
`("d"y)/("d"x) = tan^2(x + y)`
Solve the following differential equation:
`(y^2 - 2xy) "d"x = (x^2 - 2xy) "d"y`
Choose the correct alternative:
The solution of the differential equation `("d"y)/("d"x) = y/x + (∅(y/x))/(∅(y/x))` is
Choose the correct alternative:
If sin x is the integrating factor of the linear differential equation `("d"y)/("d"x) + "P"y = "Q"`, then P is
Solve: `log(("d"y)/("d"x))` = ax + by
Find the curve whose gradient at any point P(x, y) on it is `(x - "a")/(y - "b")` and which passes through the origin
Solve the following homogeneous differential equation:
The slope of the tangent to a curve at any point (x, y) on it is given by (y3 – 2yx2) dx + (2xy2 – x3) dy = 0 and the curve passes through (1, 2). Find the equation of the curve
Solve the following homogeneous differential equation:
An electric manufacturing company makes small household switches. The company estimates the marginal revenue function for these switches to be (x2 + y2) dy = xy dx where x represents the number of units (in thousands). What is the total revenue function?
Solve the following:
`x ("d"y)/("d"x) + 2y = x^4`
