Advertisements
Advertisements
प्रश्न
Solve the following differential equation:
(ey + 1)cos x dx + ey sin x dy = 0
Advertisements
उत्तर
(ey + 1) cos x dx + ey sin x dy = 0
ey sin x dy = – (ey + 1) cos x dx
`int ("e"^y "d"y)/("e"^y + 1) =-int (cosx "d"x)/sin x`
log (ey + 1) = – log sin x + log c
log [(ey + 1) + log sin x = log c
log (ey +1) sin x] = log c
(ey+ 1) sin x = c
APPEARS IN
संबंधित प्रश्न
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
Solve the following differential equation:
`("d"y)/("d"x) = sqrt((1 - y^2)/(1 - x^2)`
Solve the following differential equation:
`[x + y cos(y/x)] "d"x = x cos(y/x) "d"y`
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
Choose the correct alternative:
The solution of `("d"y)/("d"x) + "p"(x)y = 0` is
Choose the correct alternative:
The general solution of the differential equation `log(("d"y)/("d"x)) = x + y` is
Choose the correct alternative:
The solution of the differential equation `("d"y)/("d"x) = y/x + (∅(y/x))/(∅(y/x))` is
Choose the correct alternative:
The number of arbitrary constants in the particular solution of a differential equation of third order is
Solve: (1 – x) dy – (1 + y) dx = 0
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:
`("d"y)/("d"x) + (3x^2)/(1 + x^3) y = (1 + x^2)/(1 + x^3)`
Solve the following:
`("d"y)/("d"x) + y tan x = cos^3x`
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:
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:
The variable separable form of `("d"y)/("d"x) = (y(x - y))/(x(x + y))` by taking y = vx and `("d"y)/("d"x) = "v" + x "dv"/("d"x)` is
Form the differential equation having for its general solution y = ax2 + bx
Solve `x ("d"y)/(d"x) + 2y = x^4`
