Advertisements
Advertisements
प्रश्न
Form the differential equation from the relation x2 + 4y2 = 4b2
Advertisements
उत्तर
Given relation is
x2 + 4y2 = 4b2
Differentiating w.r.t. x, we get
`2x + 4.2y ("d"y)/("d"x) = 0`
∴ `x + 4y ("d"y)/("d"x) = 0`, which is the required differential equation.
APPEARS IN
संबंधित प्रश्न
Solve the equation for x: `sin^(-1) 5/x + sin^(-1) 12/x = π/2, x ≠ 0`
Form the differential equation representing the family of ellipses having centre at the origin and foci on x-axis.
(1 − x2) dy + xy dx = xy2 dx
(y2 + 1) dx − (x2 + 1) dy = 0
Find the particular solution of the differential equation \[\frac{dy}{dx} = - 4x y^2\] given that y = 1, when x = 0.
3x2 dy = (3xy + y2) dx
Solve the following differential equations:
\[\frac{dy}{dx} = \frac{y}{x}\left\{ \log y - \log x + 1 \right\}\]
If the interest is compounded continuously at 6% per annum, how much worth Rs 1000 will be after 10 years? How long will it take to double Rs 1000?
At every point on a curve the slope is the sum of the abscissa and the product of the ordinate and the abscissa, and the curve passes through (0, 1). Find the equation of the curve.
If sin x is an integrating factor of the differential equation \[\frac{dy}{dx} + Py = Q\], then write the value of P.
The differential equation \[x\frac{dy}{dx} - y = x^2\], has the general solution
Which of the following differential equations has y = C1 ex + C2 e−x as the general solution?
Form the differential equation representing the family of curves y = a sin (x + b), where a, b are arbitrary constant.
Form the differential equation of the family of circles having centre on y-axis and radius 3 unit.
Solve the following differential equation.
`dy/dx = x^2 y + y`
Solve the following differential equation.
`(dθ)/dt = − k (θ − θ_0)`
Solve the following differential equation.
y dx + (x - y2 ) dy = 0
Solve the following differential equation.
`dy/dx + 2xy = x`
Solve `("d"y)/("d"x) = (x + y + 1)/(x + y - 1)` when x = `2/3`, y = `1/3`
State whether the following statement is True or False:
The integrating factor of the differential equation `("d"y)/("d"x) - y` = x is e–x
The differential equation (1 + y2)x dx – (1 + x2)y dy = 0 represents a family of:
