Advertisements
Advertisements
प्रश्न
Choose the correct alternative:
Solution of the equation `x("d"y)/("d"x)` = y log y is
विकल्प
y = aex
y = be2x
y = be–2x
y = eax
Advertisements
उत्तर
y = eax
APPEARS IN
संबंधित प्रश्न
Verify that y = \[\frac{a}{x} + b\] is a solution of the differential equation
\[\frac{d^2 y}{d x^2} + \frac{2}{x}\left( \frac{dy}{dx} \right) = 0\]
Differential equation \[\frac{d^2 y}{d x^2} + y = 0, y \left( 0 \right) = 0, y' \left( 0 \right) = 1\] Function y = sin x
Differential equation \[\frac{d^2 y}{d x^2} - \frac{dy}{dx} = 0, y \left( 0 \right) = 2, y'\left( 0 \right) = 1\]
Function y = ex + 1
Differential equation \[\frac{d^2 y}{d x^2} - 3\frac{dy}{dx} + 2y = 0, y \left( 0 \right) = 1, y' \left( 0 \right) = 3\] Function y = ex + e2x
(y + xy) dx + (x − xy2) dy = 0
Solve the following differential equations:
\[\frac{dy}{dx} = \frac{y}{x}\left\{ \log y - \log x + 1 \right\}\]
The rate of increase of bacteria in a culture is proportional to the number of bacteria present and it is found that the number doubles in 6 hours. Prove that the bacteria becomes 8 times at the end of 18 hours.
Define a differential equation.
Which of the following transformations reduce the differential equation \[\frac{dz}{dx} + \frac{z}{x}\log z = \frac{z}{x^2} \left( \log z \right)^2\] into the form \[\frac{du}{dx} + P\left( x \right) u = Q\left( x \right)\]
The differential equation
\[\frac{dy}{dx} + Py = Q y^n , n > 2\] can be reduced to linear form by substituting
What is integrating factor of \[\frac{dy}{dx}\] + y sec x = tan x?
Integrating factor of the differential equation cos \[x\frac{dy}{dx} + y \sin x = 1\], is
In the following verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation:-
y = ex + 1 y'' − y' = 0
Determine the order and degree of the following differential equations.
| Solution | D.E. |
| y = 1 − logx | `x^2(d^2y)/dx^2 = 1` |
Solve the following differential equation.
x2y dx − (x3 + y3) dy = 0
Solve the following differential equation.
y dx + (x - y2 ) dy = 0
y2 dx + (xy + x2)dy = 0
Solve the following differential equation y2dx + (xy + x2) dy = 0
The differential equation of all non horizontal lines in a plane is `("d"^2x)/("d"y^2)` = 0
If `y = log_2 log_2(x)` then `(dy)/(dx)` =
