Advertisements
Advertisements
प्रश्न
\[\frac{dy}{dx} - y \tan x = - 2 \sin x\]
Advertisements
उत्तर
We have,
\[\frac{dy}{dx} - y \tan x = - 2\sin x\]
\[\text{Comparing with }\frac{dy}{dx} + Py = Q,\text{ we get}\]
\[P = - \tan x \]
\[Q = - 2\sin x\]
\[Now, \]
\[I . F . = e^{\int - \tan x\ dx} \]
\[ = e^{- \log\left| \left( \sec x \right) \right|} \]
\[ = e^{\log\left| \left( \cos x \right) \right|} \]
\[ = \cos x\]
So, the solution is given by
\[y \cos x = - \int\left( 2\sin x \cos x \right) dx + C\]
\[ \Rightarrow y \cos x = - \int\sin 2x\ dx + C\]
\[ \therefore y \cos x = \frac{\cos 2x}{2} + C\]
APPEARS IN
संबंधित प्रश्न
Solve the differential equation cos(x +y) dy = dx hence find the particular solution for x = 0 and y = 0.
The differential equation of `y=c/x+c^2` is :
(a)`x^4(dy/dx)^2-xdy/dx=y`
(b)`(d^2y)/dx^2+xdy/dx+y=0`
(c)`x^3(dy/dx)^2+xdy/dx=y`
(d)`(d^2y)/dx^2+dy/dx-y=0`
Verify that the given function (explicit or implicit) is a solution of the corresponding differential equation:
y = Ax : xy′ = y (x ≠ 0)
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
Find a particular solution of the differential equation`(x + 1) dy/dx = 2e^(-y) - 1`, given that y = 0 when x = 0.
The general solution of the differential equation \[\frac{dy}{dx} + y\] g' (x) = g (x) g' (x), where g (x) is a given function of x, is
The solution of the differential equation x dx + y dy = x2 y dy − y2 x dx, is
The solution of the differential equation (x2 + 1) \[\frac{dy}{dx}\] + (y2 + 1) = 0, is
The general solution of the differential equation \[\frac{y dx - x dy}{y} = 0\], is
The general solution of a differential equation of the type \[\frac{dx}{dy} + P_1 x = Q_1\] is
The general solution of the differential equation ex dy + (y ex + 2x) dx = 0 is
Find the general solution of the differential equation \[x \cos \left( \frac{y}{x} \right)\frac{dy}{dx} = y \cos\left( \frac{y}{x} \right) + x .\]
x (e2y − 1) dy + (x2 − 1) ey dx = 0
\[\frac{dy}{dx} = \frac{y\left( x - y \right)}{x\left( x + y \right)}\]
\[\frac{dy}{dx} - y \cot x = cosec\ x\]
(x2 + 1) dy + (2y − 1) dx = 0
\[x\frac{dy}{dx} + x \cos^2 \left( \frac{y}{x} \right) = y\]
\[y^2 + \left( x + \frac{1}{y} \right)\frac{dy}{dx} = 0\]
Solve the following differential equation:- \[x \cos\left( \frac{y}{x} \right)\frac{dy}{dx} = y \cos\left( \frac{y}{x} \right) + x\]
Solve the following differential equation:-
(1 + x2) dy + 2xy dx = cot x dx
Solve the following differential equation:-
y dx + (x − y2) dy = 0
Solve the differential equation: ` ("x" + 1) (d"y")/(d"x") = 2e^-"y" - 1; y(0) = 0.`
y = x is a particular solution of the differential equation `("d"^2y)/("d"x^2) - x^2 "dy"/"dx" + xy` = x.
Find the general solution of `(x + 2y^3) "dy"/"dx"` = y
Solve:
`2(y + 3) - xy (dy)/(dx)` = 0, given that y(1) = – 2.
Find the general solution of (1 + tany)(dx – dy) + 2xdy = 0.
Find the general solution of `("d"y)/("d"x) -3y = sin2x`
y = aemx+ be–mx satisfies which of the following differential equation?
The solution of the differential equation cosx siny dx + sinx cosy dy = 0 is ______.
The differential equation for which y = acosx + bsinx is a solution, is ______.
The solution of `("d"y)/("d"x) + y = "e"^-x`, y(0) = 0 is ______.
Solution of the differential equation `("d"y)/("d"x) + y/x` = sec x is ______.
The solution of the differential equation `x(dy)/("d"x) + 2y = x^2` is ______.
General solution of `("d"y)/("d"x) + y` = sinx is ______.
The integrating factor of `("d"y)/("d"x) + y = (1 + y)/x` is ______.
Polio drops are delivered to 50 K children in a district. The rate at which polio drops are given is directly proportional to the number of children who have not been administered the drops. By the end of 2nd week half the children have been given the polio drops. How many will have been given the drops by the end of 3rd week can be estimated using the solution to the differential equation `"dy"/"dx" = "k"(50 - "y")` where x denotes the number of weeks and y the number of children who have been given the drops.
The value of c in the particular solution given that y(0) = 0 and k = 0.049 is ______.
Find the general solution of the differential equation:
`(dy)/(dx) = (3e^(2x) + 3e^(4x))/(e^x + e^-x)`
