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
Solve the following differential equation:
`y"d"x + (1 + x^2)tan^-1x "d"y`= 0
Solve the following differential equation:
`(y^2 - 2xy) "d"x = (x^2 - 2xy) "d"y`
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 `("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:
If sin x is the integrating factor of the linear differential equation `("d"y)/("d"x) + "P"y = "Q"`, then P is
Solve: `("d"y)/("d"x) = "ae"^y`
Solve: `(1 + x^2)/(1 + y) = xy ("d"y)/("d"x)`
Solve: `("d"y)/("d"x) + "e"^x + y"e"^x = 0`
Solve: (1 – x) dy – (1 + y) dx = 0
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 homogeneous differential equation:
The slope of the tangent to a curve at any point (x, y) on it is given by (y3 – 2yx2) dx + (2xy2 – x3) dy = 0 and the curve passes through (1, 2). Find the equation of the curve
Solve the following:
`("d"y)/("d"x) + y tan x = cos^3x`
Choose the correct alternative:
If y = ex + c – c3 then its differential equation is
Choose the correct alternative:
The differential equation of y = mx + c is (m and c are arbitrary constants)
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 solution of the differential equation `("d"y)/("d"x) = y/x + (f(y/x))/(f"'"(y/x))` is
Solve `("d"y)/("d"x) = xy + x + y + 1`
