Advertisements
Advertisements
प्रश्न
Solve the following differential equation:
`sin ("d"y)/("d"x)` = a, y(0) = 1
उत्तर
`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
संबंधित प्रश्न
The velocity v, of a parachute falling vertically satisfies the equation `"v" (dv)/(dx) = "g"(1 - v^2/k^2)` where g and k are constants. If v and are both initially zero, find v in terms of x
Solve the following differential equation:
`(ydx - xdy) cot (x/y)` = ny2 dx
Solve the following differential equation:
`("d"y)/("d"x) = tan^2(x + y)`
Solve the following differential equation:
`2xy"d"x + (x^2 + 2y^2)"d"y` = 0
Choose the correct alternative:
The solution of `("d"y)/("d"x) = 2^(y - x)` is
Solve: `y(1 - x) - x ("d"y)/("d"x)` = 0
Solve: `log(("d"y)/("d"x))` = ax + by
Solve the following homogeneous differential equation:
`(x - y) ("d"y)/("d"x) = x + 3y`
Solve the following homogeneous differential equation:
`x ("d"y)/("d"x) - y = sqrt(x^2 + y^2)`
Solve the following:
`x ("d"y)/("d"x) + 2y = x^4`
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:
If y = ex + c – c3 then its differential equation is
Choose the correct alternative:
The solution of the differential equation `("d"y)/("d"x) + "P"y` = Q where P and Q are the function of x is
Choose the correct alternative:
Which of the following is the homogeneous differential equation?
Choose the correct alternative:
The solution of the differential equation `("d"y)/("d"x) = y/x + (f(y/x))/(f"'"(y/x))` is
Form the differential equation having for its general solution y = ax2 + bx
Solve (x2 + y2) dx + 2xy dy = 0
Solve `("d"y)/("d"x) + y cos x + x = 2 cos x`
Solve `("d"y)/("d"x) = xy + x + y + 1`
