Advertisements
Advertisements
प्रश्न
Verify y = log x + c is the solution of differential equation `x ("d"^2y)/("d"x^2) + ("d"y)/("d"x)` = 0
Advertisements
उत्तर
y = log x + c
Differentiating w.r.t. x, we get
`("d"y)/("d"x) = 1/x`
∴ `x ("d"y)/("d"x)` = 1
Again, differentiating w.r.t. x, we get
`x ("d"^2y)/("d"x^2) + ("d"y)/("d"x)` = 0
∴ Given function is a solution of the given differential equation.
APPEARS IN
संबंधित प्रश्न
For the following differential equation verify that the accompanying function is a solution:
| Differential equation | Function |
|
\[x\frac{dy}{dx} + y = y^2\]
|
\[y = \frac{a}{x + a}\]
|
Differential equation \[\frac{d^2 y}{d x^2} + y = 0, y \left( 0 \right) = 0, y' \left( 0 \right) = 1\] Function y = sin x
xy dy = (y − 1) (x + 1) dx
Solve the following differential equation:
\[y e^\frac{x}{y} dx = \left( x e^\frac{x}{y} + y^2 \right)dy, y \neq 0\]
Find the solution of the differential equation cos y dy + cos x sin y dx = 0 given that y = \[\frac{\pi}{2}\], when x = \[\frac{\pi}{2}\]
\[x^2 \frac{dy}{dx} = x^2 + xy + y^2 \]
Find the equation of the curve which passes through the point (3, −4) and has the slope \[\frac{2y}{x}\] 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.
The solution of the differential equation y1 y3 = y22 is
If a + ib = `("x" + "iy")/("x" - "iy"),` prove that `"a"^2 +"b"^2 = 1` and `"b"/"a" = (2"xy")/("x"^2 - "y"^2)`
Find the particular solution of the differential equation `"dy"/"dx" = "xy"/("x"^2+"y"^2),`given that y = 1 when x = 0
Solve the following differential equation.
y2 dx + (xy + x2 ) dy = 0
Solve the following differential equation.
`dy/dx + 2xy = x`
Solve the following differential equation.
dr + (2r)dθ= 8dθ
The differential equation of `y = k_1e^x+ k_2 e^-x` is ______.
Solve:
(x + y) dy = a2 dx
Solve the differential equation `("d"y)/("d"x) + y` = e−x
Choose the correct alternative:
General solution of `y - x ("d"y)/("d"x)` = 0 is
The function y = cx is the solution of differential equation `("d"y)/("d"x) = y/x`
A man is moving away from a tower 41.6 m high at a rate of 2 m/s. If the eye level of the man is 1.6 m above the ground, then the rate at which the angle of elevation of the top of the tower changes, when he is at a distance of 30 m from the foot of the tower, is
