Advertisements
Advertisements
Question
Solve the following differential equation:
`sin ("d"y)/("d"x)` = a, y(0) = 1
Advertisements
Solution
`sin ("d"y)/("d"x)` = a
`sin ("d"y)/("d"x)` = sin–1(a)
The equation can be written as
dy = sin–1(a) dx
Taking integration on both sides, we get
`int "d"y = int sin^-1 ("a") "d"x`
y = `sin^-1 "a" int "d"x`
y = sin–1(a) x + C ........(1)
Initial condition:
Since y (0) = 1, we get
y = sin–1(a) x + C
1 = sin–1(a) (0) + C
0 + C = 1
C = 1
Equation (1)
⇒ y = sin–1(a) x + 1
y – 1 = sin–1(a) x
`(y - 1)/x` = sin–1(a)
`sin((y - 1)/x)` = a
APPEARS IN
RELATED QUESTIONS
If F is the constant force generated by the motor of an automobile of mass M, its velocity V is given by `"M""dv"/"dt"` = F – kV, where k is a constant. Express V in terms of t given that V = 0 when t = 0
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:
x cos y dy = ex(x log x + 1) dx
Solve the following differential equation:
`(x^3 + y^3)"d"y - x^2 y"d"x` = 0
Solve the following differential equation:
`y"e"^(x/y) "d"x = (x"e"^(x/y) + y) "d"y`
Solve: `("d"y)/("d"x) = "ae"^y`
Solve: `(1 + x^2)/(1 + y) = xy ("d"y)/("d"x)`
Solve: (1 – x) dy – (1 + y) dx = 0
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:
`("d"y)/("d"x) + (3x^2)/(1 + x^3) y = (1 + x^2)/(1 + x^3)`
Choose the correct alternative:
The differential equation of x2 + y2 = a2
Choose the correct alternative:
A homogeneous differential equation of the form `("d"x)/("d"y) = f(x/y)` can be solved by making substitution
Choose the correct alternative:
Which of the following is the homogeneous differential equation?
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
