Advertisements
Advertisements
प्रश्न
\[\frac{dy}{dx} = \frac{1}{x^2 + 4x + 5}\]
Advertisements
उत्तर
We have,
\[\frac{dy}{dx} = \frac{1}{x^2 + 4x + 5}\]
\[ \Rightarrow \frac{dy}{dx} = \frac{1}{x^2 + 4x + 4 + 1}\]
\[ \Rightarrow \frac{dy}{dx} = \frac{1}{\left( x + 2 \right)^2 + \left( 1 \right)^2}\]
\[ \Rightarrow dy = \frac{1}{\left( x + 2 \right)^2 + \left( 1 \right)^2}dx\]
Integrating both sides, we get
\[\int y = \int\frac{1}{\left( x + 2 \right)^2 + \left( 1 \right)^2}dx\]
\[ \Rightarrow y = \tan^{- 1} \frac{x + 2}{1} + C\]
\[ \Rightarrow y = \tan^{- 1} \left( x + 2 \right) + C\]
APPEARS IN
संबंधित प्रश्न
Find the differential equation of the family of lines passing through the origin.
Find the differential equation representing the family of curves v=A/r+ B, where A and B are arbitrary constants.
Form a differential equation representing the given family of curves by eliminating arbitrary constants a and b.
y = e2x (a + bx)
Solve the differential equation `ye^(x/y) dx = (xe^(x/y) + y^2)dy, (y != 0)`
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 the differential equation ex dy + (y ex + 2x) dx = 0 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.
\[\frac{dy}{dx} = \sin^3 x \cos^4 x + x\sqrt{x + 1}\]
\[\frac{dy}{dx} + 4x = e^x\]
\[\frac{dy}{dx} = x^2 e^x\]
\[\frac{dy}{dx} - x \sin^2 x = \frac{1}{x \log x}\]
\[\frac{dy}{dx} = \sin^3 x \cos^2 x + x e^x\]
tan y dx + tan x dy = 0
(1 + x) y dx + (1 + y) x dy = 0
cosec x (log y) dy + x2y dx = 0
Find the general solution of the differential equation `"dy"/"dx" = y/x`.
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)`
General solution of tan 5θ = cot 2θ is
Solution of the equation 3 tan(θ – 15) = tan(θ + 15) is
Find the general solution of differential equation `(dy)/(dx) = (1 - cosx)/(1 + cosx)`
What is the general solution of differential equation `(dy)/(dx) = sqrt(4 - y^2) (-2 < y < 2)`
