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) = 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:
`("d"y)/("d"x) = tan^2(x + y)`
Solve the following differential equation:
`(1 + 3"e"^(y/x))"d"y + 3"e"^(y/x)(1 - y/x)"d"x` = 0, given that y = 0 when x = 1
Choose the correct alternative:
The general solution of the differential equation `log(("d"y)/("d"x)) = x + y` is
Solve : cos x(1 + cosy) dx – sin y(1 + sinx) dy = 0
Solve: (1 – x) dy – (1 + y) dx = 0
Solve the following homogeneous differential equation:
The slope of the tangent to a curve at any point (x, y) on it is given by (y3 – 2yx2) dx + (2xy2 – x3) dy = 0 and the curve passes through (1, 2). Find the equation of the curve
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:
The variable separable form of `("d"y)/("d"x) = (y(x - y))/(x(x + y))` by taking y = vx and `("d"y)/("d"x) = "v" + x "dv"/("d"x)` is
