Advertisements
Advertisements
प्रश्न
Solve the following differential equation:
`y"d"x + (1 + x^2)tan^-1x "d"y`= 0
उत्तर
`y"d"x + (1 + x^2)tan^-1x "d"y`
Take t = tan–1x
dt `1/(1 + x^2) "d"x`
The equation can be written as
`("d"x)/((1 + x^2)tan^-) = - ("d"y)/y`
`"dt"/"t" = - ("d"y)/y`
Taking Integration on both sides, we get
`int "dt"/"t" = int ("d"y)/y`
log t = – log y + log C
log(tan–1x) = – log y + log C
log (y(tan–1x)) + log y = log C
y tan–1x = 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) = tan^2(x + y)`
Solve the following differential equation:
`[x + y cos(y/x)] "d"x = x cos(y/x) "d"y`
Solve the following differential equation:
`2xy"d"x + (x^2 + 2y^2)"d"y` = 0
Solve the following differential equation:
`(1 + 3"e"^(y/x))"d"y + 3"e"^(y/x)(1 - y/x)"d"x` = 0, given that y = 0 when x = 1
Solve the following differential equation:
(x2 + y2) dy = xy dx. It is given that y (1) = y(x0) = e. Find the value of x0
Choose the correct alternative:
The solution of the differential equation `("d"y)/("d"x) = y/x + (∅(y/x))/(∅(y/x))` is
Solve: `(1 + x^2)/(1 + y) = xy ("d"y)/("d"x)`
Solve: (1 – x) dy – (1 + y) dx = 0
Solve: `("d"y)/("d"x) = y sin 2x`
Solve the following homogeneous differential equation:
`("d"y)/("d"x) = (3x - 2y)/(2x - 3y)`
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:
If `("d"y)/("d"x) + 2 y tan x = sin x` and if y = 0 when x = `pi/3` express y in term of x
Solve the following:
`("d"y)/("d"x) + y/x = x"e"^x`
Choose the correct alternative:
If sec2 x is an integrating factor of the differential equation `("d"y)/("d"x) + "P"y` = Q then P =
Choose the correct alternative:
A homogeneous differential equation of the form `("d"y)/("d"x) = f(y/x)` can be solved by making substitution
Choose the correct alternative:
Which of the following is the homogeneous differential equation?
Solve `x ("d"y)/(d"x) + 2y = x^4`
