Advertisements
Advertisements
प्रश्न
Find the differential equation whose general solution is
x3 + y3 = 35ax.
Advertisements
उत्तर
x3 + y3 = 35ax ...(i)
Differentiating w.r.t. x, we get
`3x^3 + 3y^3 dy/dx = 35a` ...(ii)
Substituting (ii) in (i), we get
`x^3 + y^3 = (3x^2 + 3y^2 dy/dx)x`
∴ `x^3 + y^3 = 3x^3 + 3x*y^2 dy/dx`
∴ `2x^3 - y^3 +3xy^2dy/dx =0`, which is the required differential equation.
संबंधित प्रश्न
Verify that y2 = 4ax is a solution of the differential equation y = x \[\frac{dy}{dx} + a\frac{dx}{dy}\]
Show that y = e−x + ax + b is solution of the differential equation\[e^x \frac{d^2 y}{d x^2} = 1\]
Differential equation \[\frac{d^2 y}{d x^2} + y = 0, y \left( 0 \right) = 1, y' \left( 0 \right) = 1\] Function y = sin x + cos x
xy dy = (y − 1) (x + 1) dx
dy + (x + 1) (y + 1) dx = 0
Solve the following differential equation:
\[y\left( 1 - x^2 \right)\frac{dy}{dx} = x\left( 1 + y^2 \right)\]
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:
\[x\frac{dy}{dx} + y = x \cos x + \sin x, y\left( \frac{\pi}{2} \right) = 1\]
Solve the following initial value problem:-
\[\frac{dy}{dx} + 2y \tan x = \sin x; y = 0\text{ when }x = \frac{\pi}{3}\]
The population of a city increases at a rate proportional to the number of inhabitants present at any time t. If the population of the city was 200000 in 1990 and 250000 in 2000, what will be the population in 2010?
The decay rate of radium at any time t is proportional to its mass at that time. Find the time when the mass will be halved of its initial mass.
Show that the equation of the curve whose slope at any point is equal to y + 2x and which passes through the origin is y + 2 (x + 1) = 2e2x.
The tangent at any point (x, y) of a curve makes an angle tan−1(2x + 3y) with x-axis. Find the equation of the curve if it passes through (1, 2).
Find the coordinates of the centre, foci and equation of directrix of the hyperbola x2 – 3y2 – 4x = 8.
Find the equation of the plane passing through the point (1, -2, 1) and perpendicular to the line joining the points A(3, 2, 1) and B(1, 4, 2).
Solve the following differential equation.
`dy/dx + y = e ^-x`
Choose the correct alternative.
The integrating factor of `dy/dx - y = e^x `is ex, then its solution is
`xy dy/dx = x^2 + 2y^2`
Solve the following differential equation y log y = `(log y - x) ("d"y)/("d"x)`
Solve the following differential equation
`x^2 ("d"y)/("d"x)` = x2 + xy − y2
Verify y = log x + c is the solution of differential equation `x ("d"^2y)/("d"x^2) + ("d"y)/("d"x)` = 0
Solve the differential equation `"dy"/"dx" + 2xy` = y
`d/(dx)(tan^-1 (sqrt(1 + x^2) - 1)/x)` is equal to:
