Advertisements
Advertisements
Question
Solve: `("d"y)/("d"x) = "ae"^y`
Advertisements
Solution
`("d"y)/("d"x) = "ae"^y`
`("d"y)/"e"^y` = adx
⇒ e–y dy = adx
Integrating on both sides
` int "e"^y "d"y = int "ad"x`
`"e"^y/((-1))` = ax + c
– e–y = ax + c
⇒ e–y + ax + c = 0
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
Solve the following differential equation:
(ey + 1)cos x dx + ey sin x dy = 0
Solve the following differential equation:
`tan y ("d"y)/("d"x) = cos(x + y) + cos(x - y)`
Solve the following differential equation:
`(x^3 + y^3)"d"y - x^2 y"d"x` = 0
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 number of arbitrary constants in the particular solution of a differential equation of third order is
Solve: `("d"y)/("d"x) + "e"^x + y"e"^x = 0`
Solve the following homogeneous differential equation:
`("d"y)/("d"x) = (3x - 2y)/(2x - 3y)`
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 (x2 + y2) dx + 2xy dy = 0
