Advertisements
Advertisements
प्रश्न
Write the solution of the differential equation \[\frac{dy}{dx} = 2^{- y}\] .
उत्तर
We have
\[\frac{dy}{dx} = 2^{- y} \]
\[ \Rightarrow \frac{dy}{2^{- y}} = dx\]
\[ \Rightarrow 2^y dy = dx\]
Integrating both sides, we get
\[\int 2^y dy = \int dx\]
\[ \Rightarrow \frac{2^y}{\log2} = x + c\]
\[ \Rightarrow 2^y = x\log2 + k, \text { where } k = c\log2\]
APPEARS IN
संबंधित प्रश्न
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.
Verify that the given function (explicit or implicit) is a solution of the corresponding differential equation:
y – cos y = x : (y sin y + cos y + x) y′ = y
Verify that the given function (explicit or implicit) is a solution of the corresponding differential equation:
x + y = tan–1y : y2 y′ + y2 + 1 = 0
Find `(dy)/(dx)` at x = 1, y = `pi/4` if `sin^2 y + cos xy = K`
Find the differential equation of the family of concentric circles `x^2 + y^2 = a^2`
The solution of the differential equation \[2x\frac{dy}{dx} - y = 3\] represents
The solution of the differential equation \[x\frac{dy}{dx} = y + x \tan\frac{y}{x}\], is
The number of arbitrary constants in the particular solution of a differential equation of third order is
Solve the differential equation (x2 − yx2) dy + (y2 + x2y2) dx = 0, given that y = 1, when x = 1.
\[\frac{dy}{dx} = \left( x + y \right)^2\]
\[\frac{dy}{dx} + \frac{y}{x} = \frac{y^2}{x^2}\]
\[\frac{dy}{dx} - y \tan x = e^x\]
(x2 + 1) dy + (2y − 1) dx = 0
\[\frac{dy}{dx} + 2y = \sin 3x\]
Solve the following differential equation:-
\[x \log x\frac{dy}{dx} + y = \frac{2}{x}\log x\]
Find the equation of a curve passing through the point (0, 0) and whose differential equation is \[\frac{dy}{dx} = e^x \sin x.\]
The solution of the differential equation `x "dt"/"dx" + 2y` = x2 is ______.
y = x is a particular solution of the differential equation `("d"^2y)/("d"x^2) - x^2 "dy"/"dx" + xy` = x.
If y(x) is a solution of `((2 + sinx)/(1 + y))"dy"/"dx"` = – cosx and y (0) = 1, then find the value of `y(pi/2)`.
If y(t) is a solution of `(1 + "t")"dy"/"dt" - "t"y` = 1 and y(0) = – 1, then show that y(1) = `-1/2`.
Find the general solution of y2dx + (x2 – xy + y2) dy = 0.
Solve: `2(y + 3) - xy "dy"/"dx"` = 0, given that y(1) = – 2.
The number of solutions of `("d"y)/("d"x) = (y + 1)/(x - 1)` when y (1) = 2 is ______.
The general solution of the differential equation `("d"y)/("d"x) = "e"^(x^2/2) + xy` is ______.
Which of the following is the general solution of `("d"^2y)/("d"x^2) - 2 ("d"y)/("d"x) + y` = 0?
The member of arbitrary constants in the particulars solution of a differential equation of third order as
The curve passing through (0, 1) and satisfying `sin(dy/dx) = 1/2` is ______.
