Advertisements
Advertisements
प्रश्न
Write the differential equation obtained by eliminating the arbitrary constant C in the equation x2 − y2 = C2.
Advertisements
उत्तर
We have,
\[ x^2 - y^2 = C^2 \]
Differentiating with respect to x, we get
\[2x - 2y\frac{dy}{dx} = 0\]
\[ \Rightarrow 2x = 2y\frac{dy}{dx}\]
\[ \Rightarrow x dx = y dy\]
\[ \Rightarrow x dx - y dy = 0\]
Hence, x dx - y dy = 0 is the required differential equation .
APPEARS IN
संबंधित प्रश्न
If 1, `omega` and `omega^2` are the cube roots of unity, prove `(a + b omega + c omega^2)/(c + s omega + b omega^2) = omega^2`
Form the differential equation of the family of hyperbolas having foci on x-axis and centre at the origin.
Verify that y = cx + 2c2 is a solution of the differential equation
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 \[\frac{d^2 y}{d x^2} - 3\frac{dy}{dx} + 2y = 0, y \left( 0 \right) = 1, y' \left( 0 \right) = 3\] Function y = ex + e2x
xy (y + 1) dy = (x2 + 1) dx
tan y \[\frac{dy}{dx}\] = sin (x + y) + sin (x − y)
Solve the following differential equation:
\[\text{ cosec }x \log y \frac{dy}{dx} + x^2 y^2 = 0\]
Solve the following differential equation:
\[\left( 1 + y^2 \right) \tan^{- 1} xdx + 2y\left( 1 + x^2 \right)dy = 0\]
Solve the differential equation \[x\frac{dy}{dx} + \cot y = 0\] given that \[y = \frac{\pi}{4}\], when \[x=\sqrt{2}\]
Solve the differential equation \[\left( 1 + x^2 \right)\frac{dy}{dx} + \left( 1 + y^2 \right) = 0\], 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.
2xy dx + (x2 + 2y2) dy = 0
Solve the following initial value problem:-
\[\frac{dy}{dx} + 2y = e^{- 2x} \sin x, y\left( 0 \right) = 0\]
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.
Radium decomposes at a rate proportional to the quantity of radium present. It is found that in 25 years, approximately 1.1% of a certain quantity of radium has decomposed. Determine approximately how long it will take for one-half of the original amount of radium to decompose?
Find the equation of the curve that passes through the point (0, a) and is such that at any point (x, y) on it, the product of its slope and the ordinate is equal to the abscissa.
Determine the order and degree of the following differential equations.
| Solution | D.E. |
| y = 1 − logx | `x^2(d^2y)/dx^2 = 1` |
The differential equation of `y = k_1e^x+ k_2 e^-x` is ______.
Choose the correct alternative.
Bacteria increases at the rate proportional to the number present. If the original number M doubles in 3 hours, then the number of bacteria will be 4M in
Solve the differential equation:
`e^(dy/dx) = x`
Solve the following differential equation y2dx + (xy + x2) dy = 0
Choose the correct alternative:
Solution of the equation `x("d"y)/("d"x)` = y log y is
Solve the following differential equation `("d"y)/("d"x)` = x2y + y
The differential equation of all non horizontal lines in a plane is `("d"^2x)/("d"y^2)` = 0
