Advertisements
Advertisements
प्रश्न
`(x + 2y^3 ) dy/dx = y`
उत्तर
`(x + 2y^3 ) dy/dx = y dx/dy`
∴`x/y + 2y^2 = dx/dy`
∴ `dx/dy - x/y = 2y^2`
The given equation is of the form
`dx/dy + px =Q`, where, `P = -1/ y and Q = 2y^2`
∴ I.F. `= e ^(int^(pdy) = e^ (-int^(1/y dy)`
`= e ^(-logy) = e^(1/y)`
`=1/y`
∴ Solution of the given equation is
`x(I.F.) = intQ(I.F.) dy + c`
∴ `x/y =2 int y^2/y d y +c `
∴ `x/y= 2 int y dy +c `
∴ `x/y= 2 y^2/2 +c `
∴ x = y(c + y2)
APPEARS IN
संबंधित प्रश्न
For the differential equation, find the general solution:
`dy/dx + (sec x) y = tan x (0 <= x < pi/2)`
For the differential equation, find the general solution:
`cos^2 x dy/dx + y = tan x(0 <= x < pi/2)`
For the differential equation, find the general solution:
`x dy/dx + y - x + xy cot x = 0(x != 0)`
For the differential equation, find the general solution:
`(x + y) dy/dx = 1`
For the differential equation, find the general solution:
y dx + (x – y2) dy = 0
Find the equation of a curve passing through the point (0, 2) given that the sum of the coordinates of any point on the curve exceeds the magnitude of the slope of the tangent to the curve at that point by 5.
Solve the differential equation `(tan^(-1) x- y) dx = (1 + x^2) dy`
Find the integerating factor of the differential equation `xdy/dx - 2y = 2x^2` .
Solve the following differential equation:
`"dy"/"dx" + "y" * sec "x" = tan "x"`
If the slope of the tangent to the curve at each of its point is equal to the sum of abscissa and the product of the abscissa and ordinate of the point. Also, the curve passes through the point (0, 1). Find the equation of the curve.
The solution of `(1 + x^2) ("d"y)/("d"x) + 2xy - 4x^2` = 0 is ______.
The integrating factor of differential equation `(1 - y)^2 (dx)/(dy) + yx = ay(-1 < y < 1)`
State whether the following statement is true or false.
The integrating factor of the differential equation `(dy)/(dx) + y/x` = x3 is – x.
If sec x + tan x is the integrating factor of `dy/dx + Py` = Q, then value of P is ______.
The slope of the tangent to the curve x = sin θ and y = cos 2θ at θ = `π/6` is ______.
