Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
sec2 x tan y dx + sec2 y tan x dy = 0
∴ `(sec^2x)/tanx "d"x` + `(sec^2y)/tany "d"y` = 0
Integrating, we get
`int (sec^2x)/tanx "d"x` + `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
log |tan x| + `log |tan y|` = log c
∴ log |tan x . tan y| = log c
∴ tan x . tan y = c
This is the general solution.
APPEARS IN
संबंधित प्रश्न
x cos y dy = (xex log x + ex) dx
xy dy = (y − 1) (x + 1) dx
(1 − x2) dy + xy dx = xy2 dx
Solve the following differential equation:
\[\text{ cosec }x \log y \frac{dy}{dx} + x^2 y^2 = 0\]
If y(x) is a solution of the different equation \[\left( \frac{2 + \sin x}{1 + y} \right)\frac{dy}{dx} = - \cos x\] and y(0) = 1, then find the value of y(π/2).
Solve the following differential equations:
\[\frac{dy}{dx} = \frac{y}{x}\left\{ \log y - \log x + 1 \right\}\]
Solve the following initial value problem:-
\[\frac{dy}{dx} + y\cot x = 2\cos x, y\left( \frac{\pi}{2} \right) = 0\]
Experiments show that radium disintegrates at a rate proportional to the amount of radium present at the moment. Its half-life is 1590 years. What percentage will disappear in one year?
Write the differential equation obtained eliminating the arbitrary constant C in the equation xy = C2.
The differential equation of the ellipse \[\frac{x^2}{a^2} + \frac{y^2}{b^2} = C\] is
What is integrating factor of \[\frac{dy}{dx}\] + y sec x = tan x?
Solve the following differential equation.
`y^3 - dy/dx = x dy/dx`
Solve the following differential equation.
dr + (2r)dθ= 8dθ
`xy dy/dx = x^2 + 2y^2`
`dy/dx = log x`
Solve the differential equation (x2 – yx2)dy + (y2 + xy2)dx = 0
Solve the following differential equation
`x^2 ("d"y)/("d"x)` = x2 + xy − y2
Integrating factor of the differential equation `x "dy"/"dx" - y` = sinx is ______.
Solve the differential equation `"dy"/"dx"` = 1 + x + y2 + xy2, when y = 0, x = 0.
If `y = log_2 log_2(x)` then `(dy)/(dx)` =
