Advertisements
Advertisements
प्रश्न
The solution of differential equation `x^2 ("d"^2y)/("d"x^2)` = 1 is ______
Advertisements
उत्तर
y = 1 – log x
APPEARS IN
संबंधित प्रश्न
Show that Ax2 + By2 = 1 is a solution of the differential equation x \[\left\{ y\frac{d^2 y}{d x^2} + \left( \frac{dy}{dx} \right)^2 \right\} = y\frac{dy}{dx}\]
For the following differential equation verify that the accompanying function is a solution:
| Differential equation | Function |
|
\[x\frac{dy}{dx} = y\]
|
y = ax |
(y2 + 1) dx − (x2 + 1) dy = 0
In a bank principal increases at the rate of r% per year. Find the value of r if ₹100 double itself in 10 years (loge 2 = 0.6931).
Find the particular solution of the differential equation
(1 – y2) (1 + log x) dx + 2xy dy = 0, given that y = 0 when x = 1.
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.
Write the differential equation representing the family of straight lines y = Cx + 5, where C is an arbitrary constant.
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 obtained on eliminating A and B from y = A cos ωt + B sin ωt, is
What is integrating factor of \[\frac{dy}{dx}\] + y sec x = tan x?
The integrating factor of the differential equation \[x\frac{dy}{dx} - y = 2 x^2\]
Solve the following differential equation : \[\left( \sqrt{1 + x^2 + y^2 + x^2 y^2} \right) dx + xy \ dy = 0\].
Form the differential equation of the family of parabolas having vertex at origin and axis along positive y-axis.
In the following example, verify that the given function is a solution of the corresponding differential equation.
| Solution | D.E. |
| xy = log y + k | y' (1 - xy) = y2 |
In the following example, verify that the given function is a solution of the corresponding differential equation.
| Solution | D.E. |
| y = xn | `x^2(d^2y)/dx^2 - n xx (xdy)/dx + ny =0` |
Form the differential equation from the relation x2 + 4y2 = 4b2
Choose the correct alternative.
The differential equation of y = `k_1 + k_2/x` is
Choose the correct alternative.
The solution of `x dy/dx = y` log y is
`xy dy/dx = x^2 + 2y^2`
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
Solve the differential equation `dy/dx + xy = xy^2` and find the particular solution when y = 4, x = 1.
