Advertisements
Advertisements
Question
Solve `x ("d"y)/(d"x) + 2y = x^4`
Advertisements
Solution
`x ("d"y)/(d"x) + 2y = x^4`
÷ each term by x
`("d"y)/("d"x) + (2y)/x = x^2`
This is of the form `("d"y)/("d"x) + "P"y` = Q
Here P = `2/x` and Q = x3
`int "Pd"x = 2int1/x "d"x`
= 2 log x
= log x2
I.F = `"e"^(intpdx)`
=`"e"^(logx^2)`
= x2
This solution is
y(I.F) = `int "Q"x ("I.F") d"x + "c"`
y(x2) = `int (x^3 xx x^2) 'd"x + "c"`
yx2 = `int x^5 "d"x + "c"`
⇒ yx2 = `x^6/6 + "c"`
APPEARS IN
RELATED QUESTIONS
Solve the following differential equation:
`("d"y)/("d"x) - xsqrt(25 - x^2)` = 0
Solve the following differential equation:
`[x + y cos(y/x)] "d"x = x cos(y/x) "d"y`
Solve the following differential equation:
`(x^3 + y^3)"d"y - x^2 y"d"x` = 0
Choose the correct alternative:
The solution of the differential equation `("d"y)/("d"x) = y/x + (∅(y/x))/(∅(y/x))` is
Choose the correct alternative:
If sec2 x is an integrating factor of the differential equation `("d"y)/("d"x) + "P"y` = Q then P =
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
Form the differential equation having for its general solution y = ax2 + bx
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
