Advertisements
Advertisements
प्रश्न
Choose the correct alternative.
The solution of `x dy/dx = y` log y is
पर्याय
y = aex
y = be2x
y = be-2x
y = eax
Advertisements
उत्तर
The solution of `x dy/dx = y` log y is y = eax
`x dy/dx = y` log y
∴ `dy/(ylogy) = dx/x`
Integrating on both sides, we get
`int dy/(y logy) = int 1/x dx`
∴ log log(y)= log x + log a
∴ log log(y)= log xa
∴ log(y)= ax
∴ 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 \[x\frac{dy}{dx} = 1, y\left( 1 \right) = 0\]
Function y = log x
y (1 + ex) dy = (y + 1) ex dx
(y2 + 1) dx − (x2 + 1) dy = 0
Solve the following differential equation:
\[xy\frac{dy}{dx} = 1 + x + y + xy\]
Find the particular solution of the differential equation \[\frac{dy}{dx} = - 4x y^2\] given that y = 1, when x = 0.
In a culture the bacteria count is 100000. The number is increased by 10% in 2 hours. In how many hours will the count reach 200000, if the rate of growth of bacteria is proportional to the number present.
\[\frac{dy}{dx} = \frac{y}{x} + \sin\left( \frac{y}{x} \right)\]
Solve the following initial value problem:-
\[x\frac{dy}{dx} - y = \left( x + 1 \right) e^{- x} , y\left( 1 \right) = 0\]
Solve the following initial value problem:-
\[\frac{dy}{dx} + y\cot x = 2\cos x, y\left( \frac{\pi}{2} \right) = 0\]
Find the equation of the curve which passes through the point (3, −4) and has the slope \[\frac{2y}{x}\] at any point (x, y) on it.
Find the equation of the curve which passes through the point (1, 2) and the distance between the foot of the ordinate of the point of contact and the point of intersection of the tangent with x-axis is twice the abscissa of the point of contact.
Which of the following is the integrating factor of (x log x) \[\frac{dy}{dx} + y\] = 2 log x?
Solve the following differential equation : \[\left( \sqrt{1 + x^2 + y^2 + x^2 y^2} \right) dx + xy \ dy = 0\].
Show that y = ae2x + be−x is a solution of the differential equation \[\frac{d^2 y}{d x^2} - \frac{dy}{dx} - 2y = 0\]
In the following example, verify that the given function is a solution of the corresponding differential equation.
| Solution | D.E. |
| y = xn | `x^2(d^2y)/dx^2 - n xx (xdy)/dx + ny =0` |
For the following differential equation find the particular solution.
`dy/ dx = (4x + y + 1),
when y = 1, x = 0
Solve the following differential equation.
x2y dx − (x3 + y3) dy = 0
The solution of `dy/dx + x^2/y^2 = 0` is ______
`dy/dx = log x`
Select and write the correct alternative from the given option for the question
Differential equation of the function c + 4yx = 0 is
Choose the correct alternative:
Differential equation of the function c + 4yx = 0 is
