Advertisements
Advertisements
प्रश्न
Write the solution of the differential equation \[\frac{dy}{dx} = 2^{- y}\] .
Advertisements
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
Form the differential equation of the family of circles in the second quadrant and touching the coordinate axes.
Find the particular solution of the differential equation
(1 – y2) (1 + log x) dx + 2xy dy = 0, given that y = 0 when x = 1.
Verify that the given function (explicit or implicit) is a solution of the corresponding differential equation:
`y sqrt(1 + x^2) : y' = (xy)/(1+x^2)`
Verify that the given function (explicit or implicit) is a solution of the corresponding differential equation:
`y = sqrt(a^2 - x^2 ) x in (-a,a) : x + y dy/dx = 0(y != 0)`
Solve the differential equation `[e^(-2sqrtx)/sqrtx - y/sqrtx] dx/dy = 1 (x != 0).`
Find a particular solution of the differential equation`(x + 1) dy/dx = 2e^(-y) - 1`, given that y = 0 when x = 0.
The solution of the differential equation \[2x\frac{dy}{dx} - y = 3\] represents
If m and n are the order and degree of the differential equation \[\left( y_2 \right)^5 + \frac{4 \left( y_2 \right)^3}{y_3} + y_3 = x^2 - 1\], then
The solution of the differential equation \[\frac{dy}{dx} + 1 = e^{x + y}\], is
The solution of the differential equation x dx + y dy = x2 y dy − y2 x dx, is
The solution of the differential equation \[\frac{dy}{dx} - ky = 0, y\left( 0 \right) = 1\] approaches to zero when x → ∞, if
x (e2y − 1) dy + (x2 − 1) ey dx = 0
\[\frac{dy}{dx} + 5y = \cos 4x\]
\[\left( 1 + y^2 \right) + \left( x - e^{- \tan^{- 1} y} \right)\frac{dy}{dx} = 0\]
For the following differential equation, find the general solution:- \[\frac{dy}{dx} = \frac{1 - \cos x}{1 + \cos x}\]
For the following differential equation, find the general solution:- \[\frac{dy}{dx} = \left( 1 + x^2 \right)\left( 1 + y^2 \right)\]
Solve the following differential equation:-
\[\frac{dy}{dx} - y = \cos x\]
Solve the following differential equation:-
\[\left( x + 3 y^2 \right)\frac{dy}{dx} = y\]
The general solution of the differential equation `"dy"/"dx" = "e"^(x - y)` is ______.
If y = e–x (Acosx + Bsinx), then y is a solution of ______.
Integrating factor of the differential equation `cosx ("d"y)/("d"x) + ysinx` = 1 is ______.
The general solution of ex cosy dx – ex siny dy = 0 is ______.
The general solution of `("d"y)/("d"x) = 2x"e"^(x^2 - y)` is ______.
Solution of the differential equation `("d"y)/("d"x) + y/x` = sec x is ______.
The solution of the differential equation `("d"y)/("d"x) + (2xy)/(1 + x^2) = 1/(1 + x^2)^2` is ______.
The solution of the differential equation ydx + (x + xy)dy = 0 is ______.
Which of the following differential equations has `y = x` as one of its particular solution?
Find a particular solution satisfying the given condition `- cos((dy)/(dx)) = a, (a ∈ R), y` = 1 when `x` = 0
