Advertisements
Advertisements
प्रश्न
Find the differential equation whose general solution is
x3 + y3 = 35ax.
उत्तर
x3 + y3 = 35ax ...(i)
Differentiating w.r.t. x, we get
`3x^2 + 3y^2 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
x cos y dy = (xex log x + ex) dx
tan y dx + sec2 y tan x dy = 0
Solve the differential equation \[x\frac{dy}{dx} + \cot y = 0\] given that \[y = \frac{\pi}{4}\], when \[x=\sqrt{2}\]
x2 dy + y (x + y) dx = 0
In a simple circuit of resistance R, self inductance L and voltage E, the current `i` at any time `t` is given by L \[\frac{di}{dt}\]+ R i = E. If E is constant and initially no current passes through the circuit, prove that \[i = \frac{E}{R}\left\{ 1 - e^{- \left( R/L \right)t} \right\}.\]
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.
The slope of the tangent at each point of a curve is equal to the sum of the coordinates of the point. Find the curve that passes through the origin.
If sin x is an integrating factor of the differential equation \[\frac{dy}{dx} + Py = Q\], then write the value of P.
Integrating factor of the differential equation cos \[x\frac{dy}{dx} + y\] sin x = 1, is
The differential equation of the ellipse \[\frac{x^2}{a^2} + \frac{y^2}{b^2} = C\] is
Form the differential equation of the family of circles having centre on y-axis and radius 3 unit.
Find the coordinates of the centre, foci and equation of directrix of the hyperbola x2 – 3y2 – 4x = 8.
Solve the differential equation:
`"x"("dy")/("dx")+"y"=3"x"^2-2`
Solve the following differential equation.
`(x + y) dy/dx = 1`
State whether the following is True or False:
The integrating factor of the differential equation `dy/dx - y = x` is e-x
Solve the differential equation sec2y tan x dy + sec2x tan y dx = 0
Integrating factor of the differential equation `"dy"/"dx" - y` = cos x is ex.
The differential equation of all non horizontal lines in a plane is `("d"^2x)/("d"y^2)` = 0
