Advertisements
Advertisements
Question
\[\frac{dy}{dx} - y \cot x = cosec\ x\]
Advertisements
Solution
We have,
\[\frac{dy}{dx} - y \cot x = cosec\ x\]
\[\text{Comparing with }\frac{dy}{dx} + Py = Q,\text{ we get}\]
\[P = - \cot x \]
\[Q = cosec\ x\]
Now,
\[I . F . = e^{\int - \cot x\ dx} \]
\[ = e^{- \log \left| \left( \sin x \right) \right|} \]
\[ = e^{\log \left| \left(cosec\ x \right) \right|} \]
\[ = cosec x\]
So, the solution is given by
\[y\ cosec\ x = \int cosec\ x \times cosec\ x\ dx + C\]
\[ \Rightarrow y\ cosec\ x = \int {cosec}^2 x dx + C\]
\[ \Rightarrow y\ cosec\ x = - \cot x + C\]
APPEARS IN
RELATED QUESTIONS
Solve the differential equation `dy/dx=(y+sqrt(x^2+y^2))/x`
Find the particular solution of the differential equation `e^xsqrt(1-y^2)dx+y/xdy=0` , given that y=1 when x=0
Form the differential equation of the family of circles in the second quadrant and touching the coordinate axes.
Find the particular solution of the differential equation `(1+x^2)dy/dx=(e^(mtan^-1 x)-y)` , give that y=1 when x=0.
Find the particular solution of the differential equation x (1 + y2) dx – y (1 + x2) dy = 0, given that y = 1 when x = 0.
Verify that the given function (explicit or implicit) is a solution of the corresponding differential equation:
y – cos y = x : (y sin y + cos y + x) y′ = y
Verify that the given function (explicit or implicit) is a solution of the corresponding differential equation:
x + y = tan–1y : y2 y′ + y2 + 1 = 0
Solve the differential equation `[e^(-2sqrtx)/sqrtx - y/sqrtx] dx/dy = 1 (x != 0).`
Write the order of the differential equation associated with the primitive y = C1 + C2 ex + C3 e−2x + C4, where C1, C2, C3, C4 are arbitrary constants.
The solution of the differential equation \[2x\frac{dy}{dx} - y = 3\] represents
The solution of the differential equation \[x\frac{dy}{dx} = y + x \tan\frac{y}{x}\], is
The solution of the differential equation \[\frac{dy}{dx} = \frac{x^2 + xy + y^2}{x^2}\], is
The general solution of the differential equation \[\frac{dy}{dx} = e^{x + y}\], is
Find the general solution of the differential equation \[x \cos \left( \frac{y}{x} \right)\frac{dy}{dx} = y \cos\left( \frac{y}{x} \right) + x .\]
Find the particular solution of the differential equation \[\frac{dy}{dx} = \frac{x\left( 2 \log x + 1 \right)}{\sin y + y \cos y}\] given that
Solve the differential equation (x2 − yx2) dy + (y2 + x2y2) dx = 0, given that y = 1, when x = 1.
cos (x + y) dy = dx
`(2ax+x^2)(dy)/(dx)=a^2+2ax`
x2 dy + (x2 − xy + y2) dx = 0
\[\frac{dy}{dx} + y = 4x\]
\[y^2 + \left( x + \frac{1}{y} \right)\frac{dy}{dx} = 0\]
For the following differential equation, find the general solution:- \[\frac{dy}{dx} = \sin^{- 1} x\]
For the following differential equation, find the general solution:- \[\frac{dy}{dx} + y = 1\]
Solve the following differential equation:-
\[\frac{dy}{dx} + \frac{y}{x} = x^2\]
Solve the differential equation: `(d"y")/(d"x") - (2"x")/(1+"x"^2) "y" = "x"^2 + 2`
Solve the differential equation: ` ("x" + 1) (d"y")/(d"x") = 2e^-"y" - 1; y(0) = 0.`
The general solution of the differential equation `"dy"/"dx" = "e"^(x - y)` is ______.
The general solution of the differential equation x(1 + y2)dx + y(1 + x2)dy = 0 is (1 + x2)(1 + y2) = k.
Solve: `y + "d"/("d"x) (xy) = x(sinx + logx)`
If y = e–x (Acosx + Bsinx), then y is a solution of ______.
The differential equation for y = Acos αx + Bsin αx, where A and B are arbitrary constants is ______.
Solution of the differential equation tany sec2xdx + tanx sec2ydy = 0 is ______.
The solution of `("d"y)/("d"x) + y = "e"^-x`, y(0) = 0 is ______.
The solution of the differential equation `("d"y)/("d"x) + (1 + y^2)/(1 + x^2)` is ______.
The number of arbitrary constants in the general solution of a differential equation of order three is ______.
Number of arbitrary constants in the particular solution of a differential equation of order two is two.
The differential equation of all parabolas that have origin as vertex and y-axis as axis of symmetry is ______.
