Advertisements
Advertisements
प्रश्न
Find the general solution of the differential equation:
`log((dy)/(dx)) = ax + by`.
उत्तर
Given differential equation is `log((dy)/(dx)) = ax + by`
⇒ `(dy)/(dx) = e^(ax + by)`
⇒ `(dy)/(dx) = e^(ax).e^(by)`
⇒ `(dy)/(e^(by)) = e^(ax) dx`
⇒ `e^(-by) dy = e^(ax) dx`
On integrating both sides, we get
`inte^(-by)dy = inte^(ax)dx`
`e^(-by)/(-b) = e^(ax)/a + C`
⇒ `e^(ax)/a - e^(-by)/b + C` = 0
संबंधित प्रश्न
Find the particular solution of differential equation:
`dy/dx=-(x+ycosx)/(1+sinx) " given that " y= 1 " when "x = 0`
Find the general solution of the following differential equation :
`(1+y^2)+(x-e^(tan^(-1)y))dy/dx= 0`
If y = P eax + Q ebx, show that
`(d^y)/(dx^2)=(a+b)dy/dx+aby=0`
Find the particular solution of the differential equation dy/dx=1 + x + y + xy, given that y = 0 when x = 1.
The number of arbitrary constants in the general solution of a differential equation of fourth order are ______.
Solve the differential equation:
`e^(x/y)(1-x/y) + (1 + e^(x/y)) dx/dy = 0` when x = 0, y = 1
The solution of the differential equation \[\frac{dy}{dx} + \frac{2y}{x} = 0\] with y(1) = 1 is given by
The general solution of the differential equation \[\frac{dy}{dx} + y\] g' (x) = g (x) g' (x), where g (x) is a given function of x, is
The solution of the differential equation \[\frac{dy}{dx} = 1 + x + y^2 + x y^2 , y\left( 0 \right) = 0\] is
The general solution of the differential equation \[\frac{y dx - x dy}{y} = 0\], is
Solve the differential equation (x2 − yx2) dy + (y2 + x2y2) dx = 0, given that y = 1, when x = 1.
\[y - x\frac{dy}{dx} = b\left( 1 + x^2 \frac{dy}{dx} \right)\]
\[\frac{dy}{dx} + 2y = \sin 3x\]
Solve the following differential equation:- `y dx + x log (y)/(x)dy-2x dy=0`
Solve the following differential equation:-
\[\frac{dy}{dx} - y = \cos x\]
Find a particular solution of the following differential equation:- (x + y) dy + (x − y) dx = 0; y = 1 when x = 1
Solve the differential equation: ` ("x" + 1) (d"y")/(d"x") = 2e^-"y" - 1; y(0) = 0.`
The number of arbitrary constants in a particular solution of the differential equation tan x dx + tan y dy = 0 is ______.
The general solution of the differential equation x(1 + y2)dx + y(1 + x2)dy = 0 is (1 + x2)(1 + y2) = k.
Solve: `y + "d"/("d"x) (xy) = x(sinx + logx)`
Integrating factor of the differential equation `cosx ("d"y)/("d"x) + ysinx` = 1 is ______.
tan–1x + tan–1y = c is the general solution of the differential equation ______.
The solution of the differential equation `("d"y)/("d"x) + (1 + y^2)/(1 + x^2)` is ______.
The general solution of the differential equation `("d"y)/("d"x) = "e"^(x^2/2) + xy` is ______.
The solution of `("d"y)/("d"x) + y = "e"^-x`, y(0) = 0 is ______.
The general solution of the differential equation (ex + 1) ydy = (y + 1) exdx is ______.
Number of arbitrary constants in the particular solution of a differential equation of order two is two.
The member of arbitrary constants in the particulars solution of a differential equation of third order as
The differential equation of all parabolas that have origin as vertex and y-axis as axis of symmetry is ______.
