Advertisements
Advertisements
प्रश्न
Solve the following:
`("d"y)/("d"x) - y/x = x`
Advertisements
उत्तर
Given `("d"y)/("d"x) + ((-1)/x)y = x`
It is of the form `("d"y)/("d"x) + "p"y` = Q
Here P = `(-1)/x, "Q"` = x
`int "p" "d"x = int (-1)/x "d"x`
= `- log x`
= `log(1/x)`
I.F = `"e"^(int pdx)`
= `"e"^(log(1/x)`
= `1/x`
The required solution is
y(I.F) = `int "Q"("I.F") "d"x + "c"`
`y(1/x) = int x(1/x) "d"x + "c"`
`y/x = int "d"x + "c"`
∴ `y/x` = x + c
APPEARS IN
संबंधित प्रश्न
Solve the following differential equation:
`("d"y)/("d"x) = tan^2(x + y)`
Choose the correct alternative:
The solution of `("d"y)/("d"x) = 2^(y - x)` is
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: `(1 + x^2)/(1 + y) = xy ("d"y)/("d"x)`
Solve: (1 – x) dy – (1 + y) dx = 0
Solve: `("d"y)/("d"x) = y sin 2x`
Solve the following homogeneous differential equation:
(y2 – 2xy) dx = (x2 – 2xy) dy
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
Solve the following homogeneous differential equation:
An electric manufacturing company makes small household switches. The company estimates the marginal revenue function for these switches to be (x2 + y2) dy = xy dx where x represents the number of units (in thousands). What is the total revenue function?
Solve the following:
`("d"y)/("d"x) + (3x^2)/(1 + x^3) y = (1 + x^2)/(1 + x^3)`
