Advertisements
Advertisements
Question
Solve `("d"y)/("d"x) + y cos x + x = 2 cos x`
Advertisements
Solution
`("d"y)/("d"x) + y cos x + x = 2 cos x`
This is of the form `("d"y)/("d"x) + "P"y` = Q
Here P = cos x and Q = 2 cos x
`int "Pd"x = int cos x "dx` = sin x
I.F = `"e"^(intpdx)`
= `"e"^(sinx)`
The solution is
y(I.F) = `int "Q" ("I.F") "d"x+ "c"`
yesin x = `int(2 cos x) "e"^(sin x) "d"x`
yesin x = `2int"e"^"t" "dt"`
= 2`"e"^"t" + "c"`
yesin x = `2"e"^(sinx) + "c"`
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
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:
`(ydx - xdy) cot (x/y)` = ny2 dx
Choose the correct alternative:
The number of arbitrary constants in the particular solution of a differential equation of third order is
Solve the following:
`("d"y)/(""dx) + y cos x = sin x cos x`
Solve the following:
`("d"y)/("d"x) + y/x = x'e"^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:
A homogeneous differential equation of the form `("d"y)/("d"x) = f(y/x)` can be solved by making substitution
Solve (x2 + y2) dx + 2xy dy = 0
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
