Advertisements
Advertisements
प्रश्न
Choose the correct alternative.
The differential equation of y = `k_1 + k_2/x` is
विकल्प
`(d^2y)/dx^2 + 2 dy/dx = 0`
`x(d^2y)/dx^2 + 2 dy/dx = 0`
`(d^2y)/dx^2 -2 dy/dx = 0`
`x(d^2y)/dx^2 -2 dy/dx = 0`
Advertisements
उत्तर
The differential equation of `y = k_1 + k_2/x` is `x(d^2y)/dx^2 + 2 dy/dx = 0`
Explanation
`y = k_1 + k_2/x`
∴ xy = xk1 + k2
Differentiating w.r.t. x, we get
`y+x dy/dx = k_1`
Again, differentiating w.r.t. x, we get
`dy/dx + dy/dx + x (d^2y)/dx^2 = 0`
∴ `x (d^2y)/dx^2 + 2 dy/dx = 0`
APPEARS IN
संबंधित प्रश्न
Hence, the given function is the solution to the given differential equation. \[\frac{c - x}{1 + cx}\] is a solution of the differential equation \[(1+x^2)\frac{dy}{dx}+(1+y^2)=0\].
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
Find the solution of the differential equation cos y dy + cos x sin y dx = 0 given that y = \[\frac{\pi}{2}\], when x = \[\frac{\pi}{2}\]
The volume of a spherical balloon being inflated changes at a constant rate. If initially its radius is 3 units and after 3 seconds it is 6 units. Find the radius of the balloon after `t` seconds.
(x + y) (dx − dy) = dx + dy
(y2 − 2xy) dx = (x2 − 2xy) dy
Solve the following differential equations:
\[\frac{dy}{dx} = \frac{y}{x}\left\{ \log y - \log x + 1 \right\}\]
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?
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.
Define a differential equation.
Solve the following differential equation : \[y^2 dx + \left( x^2 - xy + y^2 \right)dy = 0\] .
Choose the correct option from the given alternatives:
The solution of `1/"x" * "dy"/"dx" = tan^-1 "x"` is
Solve the following differential equation.
`x^2 dy/dx = x^2 +xy - y^2`
Solve `("d"y)/("d"x) = (x + y + 1)/(x + y - 1)` when x = `2/3`, y = `1/3`
For the differential equation, find the particular solution (x – y2x) dx – (y + x2y) dy = 0 when x = 2, y = 0
Choose the correct alternative:
Solution of the equation `x("d"y)/("d"x)` = y log y is
Choose the correct alternative:
General solution of `y - x ("d"y)/("d"x)` = 0 is
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
Solve the following differential equation
sec2 x tan y dx + sec2 y tan x dy = 0
Solution: sec2 x tan y dx + sec2 y tan x dy = 0
∴ `(sec^2x)/tanx "d"x + square` = 0
Integrating, we get
`square + int (sec^2y)/tany "d"y` = log c
Each of these integral is of the type
`int ("f'"(x))/("f"(x)) "d"x` = log |f(x)| + log c
∴ the general solution is
`square + log |tan y|` = log c
∴ log |tan x . tan y| = log c
`square`
This is the general solution.
Solve the differential equation
`x + y dy/dx` = x2 + y2
