Advertisements
Advertisements
Question
Solve: `("d"y)/("d"x) = "ae"^y`
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
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:
`("d"y)/("d"x) = sqrt((1 - y^2)/(1 - x^2)`
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:
If sin x is the integrating factor of the linear differential equation `("d"y)/("d"x) + "P"y = "Q"`, then P is
Solve : cos x(1 + cosy) dx – sin y(1 + sinx) dy = 0
Solve the following:
`("d"y)/("d"x) + y/x = x"e"^x`
Choose the correct alternative:
A homogeneous differential equation of the form `("d"x)/("d"y) = f(x/y)` can be solved by making substitution