Advertisements
Advertisements
Question
tan y dx + tan x dy = 0
Solution
We have,
tan y dx + tan x dy = 0
\[\Rightarrow \tan x\frac{dy}{dx} = - \tan y \]
\[ \Rightarrow \cot y dy = - \cot x dx\]
Integrating both sides, we get
\[\int\cot y dy = - \int\cot x dx\]
\[ \Rightarrow \log \left| \sin y \right| = - \log \left| \sin x \right| + \log C\]
\[ \Rightarrow \log \left| \sin y \right| + \log \left| \sin x \right| = \log C\]
\[ \Rightarrow \log \left| \left( \sin y \right)\left( \sin x \right) \right| = \log C\]
\[ \Rightarrow \left( \sin y \right)\left( \sin x \right) = C\]
\[ \Rightarrow \sin x \sin y = C\]
APPEARS IN
RELATED QUESTIONS
Write the integrating factor of the following differential equation:
(1+y2) dx−(tan−1 y−x) dy=0
Find the differential equation of the family of lines passing through the origin.
Form a differential equation representing the given family of curves by eliminating arbitrary constants a and b.
y = e2x (a + bx)
Find a particular solution of the differential equation (x - y) (dx + dy) = dx - dy, given that y = -1, when x = 0. (Hint: put x - y = t)
The general solution of the differential equation `(y dx - x dy)/y = 0` is ______.
The general solution of a differential equation of the type `dx/dy + P_1 x = Q_1` is ______.
Find the differential equation representing the family of curves `y = ae^(bx + 5)`. where a and b are arbitrary constants.
Find the differential equation of all the circles which pass through the origin and whose centres lie on y-axis.
Find the differential equation of all the circles which pass through the origin and whose centres lie on x-axis.
Verify that xy = a ex + b e−x + x2 is a solution of the differential equation \[x\frac{d^2 y}{d x^2} + 2\frac{dy}{dx} - xy + x^2 - 2 = 0.\]
Show that y2 − x2 − xy = a is a solution of the differential equation \[\left( x - 2y \right)\frac{dy}{dx} + 2x + y = 0.\]
Verify that y = A cos x + sin x satisfies the differential equation \[\cos x\frac{dy}{dx} + \left( \sin x \right)y=1.\]
Find the differential equation corresponding to y = ae2x + be−3x + cex where a, b, c are arbitrary constants.
Show that the differential equation of all parabolas which have their axes parallel to y-axis is \[\frac{d^3 y}{d x^3} = 0.\]
From x2 + y2 + 2ax + 2by + c = 0, derive a differential equation not containing a, b and c.
\[\frac{dy}{dx} = \sin^3 x \cos^4 x + x\sqrt{x + 1}\]
\[\frac{dy}{dx} + 4x = e^x\]
\[\frac{dy}{dx} - x \sin^2 x = \frac{1}{x \log x}\]
x cos2 y dx = y cos2 x dy
cosec x (log y) dy + x2y dx = 0
A solution of the differential equation `("dy"/"dx")^2 - x "dy"/"dx" + y` = 0 is ______.
Find the general solution of the following differential equation:
`x (dy)/(dx) = y - xsin(y/x)`
The general solution of the differential equation `(dy)/(dx) + x/y` = 0 is
General solution of tan 5θ = cot 2θ is
Solution of the equation 3 tan(θ – 15) = tan(θ + 15) is
What is the general solution of differential equation `(dy)/(dx) = sqrt(4 - y^2) (-2 < y < 2)`
The general solution of the differential equation y dx – x dy = 0 is ______.
Solve the differential equation: y dx + (x – y2)dy = 0
