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
Solve the following differential equation:
`("d"y)/("d"x) = sqrt((1 - y^2)/(1 - x^2)`
Solve the following differential equation:
`sin ("d"y)/("d"x)` = a, y(0) = 1
Solve the following differential equation:
`(ydx - xdy) cot (x/y)` = ny2 dx
Solve the following differential equation:
`("d"y)/("d"x) - xsqrt(25 - x^2)` = 0
Solve the following differential equation:
x cos y dy = ex(x log x + 1) dx
Solve the following differential equation:
`[x + y cos(y/x)] "d"x = x cos(y/x) "d"y`
Solve the following differential equation:
`(y^2 - 2xy) "d"x = (x^2 - 2xy) "d"y`
Solve the following differential equation:
`x ("d"y)/("d"x) = y - xcos^2(y/x)`
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: `log(("d"y)/("d"x))` = ax + by
Solve the following:
If `("d"y)/("d"x) + 2 y tan x = sin x` and if y = 0 when x = `pi/3` express y in term of x.
Solve the following:
A bank pays interest by continuous compounding, that is by treating the interest rate as the instantaneous rate of change of principal. A man invests ₹ 1,00,000 in the bank deposit which accrues interest, 8% per year compounded continuously. How much will he get after 10 years? (e0.8 = 2.2255)
Choose the correct alternative:
The differential equation of y = mx + c is (m and c are arbitrary constants)
Choose the correct alternative:
The differential equation of x2 + y2 = a2
Choose the correct alternative:
The solution of the differential equation `("d"y)/("d"x) = y/x + (f(y/x))/(f"'"(y/x))` is
Solve (x2 + y2) dx + 2xy dy = 0
Solve `x ("d"y)/(d"x) + 2y = x^4`
A manufacturing company has found that the cost C of operating and maintaining the equipment is related to the length ’m’ of intervals between overhauls by the equation `"m"^2 "dC"/"dm" + 2"mC"` = 2 and c = 4 and when = 2. Find the relationship between C and m
Solve x2ydx – (x3 + y3) dy = 0
