Advertisements
Advertisements
प्रश्न
Choose the correct alternative.
The solution of `x dy/dx = y` log y is
विकल्प
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
Solve the equation for x: `sin^(-1) 5/x + sin^(-1) 12/x = π/2, x ≠ 0`
Assume that a rain drop evaporates at a rate proportional to its surface area. Form a differential equation involving the rate of change of the radius of the rain drop.
Verify that y = − x − 1 is a solution of the differential equation (y − x) dy − (y2 − x2) dx = 0.
tan y \[\frac{dy}{dx}\] = sin (x + y) + sin (x − y)
Find the solution of the differential equation cos y dy + cos x sin y dx = 0 given that y = \[\frac{\pi}{2}\], when x = \[\frac{\pi}{2}\]
Find the particular solution of the differential equation \[\frac{dy}{dx} = - 4x y^2\] given that y = 1, when x = 0.
If y(x) is a solution of the different equation \[\left( \frac{2 + \sin x}{1 + y} \right)\frac{dy}{dx} = - \cos x\] and y(0) = 1, then find the value of y(π/2).
x2 dy + y (x + y) dx = 0
Solve the following initial value problem:-
\[y' + y = e^x , y\left( 0 \right) = \frac{1}{2}\]
Find the equation of the curve passing through the point \[\left( 1, \frac{\pi}{4} \right)\] and tangent at any point of which makes an angle tan−1 \[\left( \frac{y}{x} - \cos^2 \frac{y}{x} \right)\] with x-axis.
Find the equation of the curve which passes through the origin and has the slope x + 3y− 1 at any point (x, y) on it.
Find the solution of the differential equation
\[x\sqrt{1 + y^2}dx + y\sqrt{1 + x^2}dy = 0\]
The differential equation
\[\frac{dy}{dx} + Py = Q y^n , n > 2\] can be reduced to linear form by substituting
The integrating factor of the differential equation \[x\frac{dy}{dx} - y = 2 x^2\]
The integrating factor of the differential equation \[\left( 1 - y^2 \right)\frac{dx}{dy} + yx = ay\left( - 1 < y < 1 \right)\] is ______.
Solve the differential equation:
`"x"("dy")/("dx")+"y"=3"x"^2-2`
Find the differential equation whose general solution is
x3 + y3 = 35ax.
Solve the following differential equation.
`x^2 dy/dx = x^2 +xy - y^2`
The solution of `dy/dx + x^2/y^2 = 0` is ______
Choose the correct alternative.
The integrating factor of `dy/dx - y = e^x `is ex, then its solution is
x2y dx – (x3 + y3) dy = 0
Solve the differential equation (x2 – yx2)dy + (y2 + xy2)dx = 0
Solve the following differential equation y log y = `(log y - x) ("d"y)/("d"x)`
Given that `"dy"/"dx"` = yex and x = 0, y = e. Find the value of y when x = 1.
