Advertisements
Advertisements
Question
Solve the following differential equation:
`("d"y)/("d"x) = sqrt((1 - y^2)/(1 - x^2)`
Advertisements
Solution
The equation can be written as
`("d"y)/sqrt(1 - y^2) = ("d"x)/sqrt(1 - x^2)`
Taking Integration on both sides, we get
`int ("d"y)/sqrt(1 - y^2) = int ("d"x)/sqrt(1 - x^2)`
sin–1y = sin–1x + C
APPEARS IN
RELATED QUESTIONS
Find the equation of the curve whose slope is `(y - 1)/(x^2 + x)` and which passes through the point (1, 0)
Solve the following differential equation:
`("d"y)/("d"x) = "e"^(x + y) - x^3"e"^y`
Solve the following differential equation:
`(y^2 - 2xy) "d"x = (x^2 - 2xy) "d"y`
Solve: `("d"y)/("d"x) + "e"^x + y"e"^x = 0`
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:
`x ("d"y)/("d"x) = x + y`
Solve the following homogeneous differential equation:
`x ("d"y)/("d"x) - y = sqrt(x^2 + y^2)`
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:
`("d"y)/("d"x) - y/x = x`
Solve the following:
`("d"y)/(""dx) + y cos x = sin x cos x`
Solve the following:
`x ("d"y)/("d"x) + 2y = x^4`
Solve the following:
`("d"y)/("d"x) + y tan x = cos^3x`
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.
Choose the correct alternative:
The differential equation of x2 + y2 = a2
Choose the correct alternative:
The solution of the differential equation `("d"y)/("d"x) = y/x + (f(y/x))/(f"'"(y/x))` is
Solve (x2 + y2) dx + 2xy dy = 0
Solve (D2 – 3D + 2)y = e4x given y = 0 when x = 0 and x = 1
Solve `("d"y)/("d"x) + y cos x + x = 2 cos x`
Solve x2ydx – (x3 + y3) dy = 0
