Advertisements
Advertisements
Question
Solve the following differential equation:
`("d"y)/("d"x) = "e"^(x + y) - x^3"e"^y`
Advertisements
Solution
`("d"y)/("d"x) "e"^(x + y) + x^3, ("e"^y)`
= ey[ex + x3]
`("d"y)/"e"^y` = dx(ex + x3)
The equation can be written as
`("d"y)/"e"^y` = (ex + x3)dx
Taking integration on both sides, we get
`int "e"^y "d"y = int ("e"^x + x^3) "d"x`
`"e"^y/(-1) = "e"^x + x^4/4 + "C"`
Where – C = C
Which is also constant
∴ `"e"^x + "e"^-y + x^4/4` = – C = C
∴ `"e"^x + "e"^-y + x^4/4` = C
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
Find the equation of the curve whose slope is `(y - 1)/(x^2 + x)` and which passes through the point (1, 0)
Solve the following differential equation:
`2xy"d"x + (x^2 + 2y^2)"d"y` = 0
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 `("d"y)/("d"x) = 2^(y - x)` is
Choose the correct alternative:
The number of arbitrary constants in the general solutions of order n and n +1are respectively
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) = "ae"^y`
Solve: `y(1 - x) - x ("d"y)/("d"x)` = 0
Solve the following homogeneous differential equation:
`x ("d"y)/("d"x) = x + y`
Solve the following homogeneous differential equation:
`("d"y)/("d"x) = (3x - 2y)/(2x - 3y)`
Solve the following homogeneous differential equation:
An electric manufacturing company makes small household switches. The company estimates the marginal revenue function for these switches to be (x2 + y2) dy = xy dx where x represents the number of units (in thousands). What is the total revenue function?
Solve the following:
`("d"y)/("d"x) - y/x = x`
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:
A homogeneous differential equation of the form `("d"y)/("d"x) = f(y/x)` can be solved by making substitution
Choose the correct alternative:
A homogeneous differential equation of the form `("d"x)/("d"y) = f(x/y)` can be solved by making substitution
Choose the correct alternative:
Which of the following is the homogeneous differential equation?
Solve `x ("d"y)/(d"x) + 2y = x^4`
Solve `("d"y)/("d"x) + y cos x + x = 2 cos x`
