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 given, find a particular solution satisfying the given condition:
`dy/dx + 2y tan x = sin x; y = 0 " when x " = pi/3`
Find the equation of the curve passing through the origin given that the slope of the tangent to the curve at any point (x, y) is equal to the sum of the coordinates of the point.
Solve the differential equation `(tan^(-1) x- y) dx = (1 + x^2) dy`
dx + xdy = e−y sec2 y dy
Find the particular solution of the differential equation \[\frac{dx}{dy} + x \cot y = 2y + y^2 \cot y, y ≠ 0\] given that x = 0 when \[y = \frac{\pi}{2}\].
Solve the differential equation \[\frac{dy}{dx}\] + y cot x = 2 cos x, given that y = 0 when x = \[\frac{\pi}{2}\] .
Solve the following differential equation:-
\[\left( 1 + x^2 \right)\frac{dy}{dx} - 2xy = \left( x^2 + 2 \right)\left( x^2 + 1 \right)\]
Find the integerating factor of the differential equation `x(dy)/(dx) - 2y = 2x^2`
Solve the following differential equation:
`"dy"/"dx" + "y"/"x" = "x"^3 - 3`
Solve the following differential equation:
`("x + a")"dy"/"dx" - 3"y" = ("x + a")^5`
Solve the following differential equation:
y dx + (x - y2) dy = 0
Find the equation of the curve which passes through the origin and has the slope x + 3y - 1 at any point (x, y) on it.
The curve passes through the point (0, 2). The sum of the coordinates of any point on the curve exceeds the slope of the tangent to the curve at any point by 5. Find the equation of the curve.
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 integrating factor of the differential equation sin y `("dy"/"dx")` = cos y(1 - x cos y) is ______.
If y = y(x) is the solution of the differential equation, `(dy)/(dx) + 2ytanx = sinx, y(π/3)` = 0, then the maximum value of the function y (x) over R is equal to ______.
The solution of the differential equation `dx/dt = (xlogx)/t` is ______.
Solve:
`xsinx dy/dx + (xcosx + sinx)y` = sin x
