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) = sqrt((1 - y^2)/(1 - x^2)`
Solve the following differential equation:
`("d"y)/("d"x) - xsqrt(25 - x^2)` = 0
Solve the following differential equation:
x cos y dy = ex(x log x + 1) dx
Solve the following differential equation:
`("d"y)/("d"x) = tan^2(x + y)`
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: `("d"y)/("d"x) = y sin 2x`
Solve the following homogeneous differential equation:
`x ("d"y)/("d"x) - y = sqrt(x^2 + y^2)`
Solve the following homogeneous differential equation:
(y2 – 2xy) dx = (x2 – 2xy) dy
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 x2ydx – (x3 + y3) dy = 0
