Advertisements
Advertisements
प्रश्न
Solve `x ("d"y)/(d"x) + 2y = x^4`
Advertisements
उत्तर
`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
संबंधित प्रश्न
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 solution of the differential equation `("d"y)/("d"x) = y/x + (∅(y/x))/(∅(y/x))` is
Solve: `("d"y)/("d"x) + "e"^x + y"e"^x = 0`
Solve: `log(("d"y)/("d"x))` = ax + by
Solve the following homogeneous differential equation:
`("d"y)/("d"x) = (3x - 2y)/(2x - 3y)`
Solve the following:
`("d"y)/("d"x) + y tan x = cos^3x`
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
Choose the correct alternative:
A homogeneous differential equation of the form `("d"x)/("d"y) = f(x/y)` can be solved by making substitution
