Advertisements
Advertisements
प्रश्न
Solve the following differential equation:-
\[\frac{dy}{dx} + 3y = e^{- 2x}\]
उत्तर
We have,
\[\frac{dy}{dx} + 3y = e^{- 2x} \]
\[\text{Comparing with }\frac{dy}{dx} + Py = Q,\text{ we get}\]
\[P = 3\]
\[Q = e^{- 2x} \]
Now,
\[I . F . = e^{\int P\ dx} \]
\[ = e^{3\int dx} \]
\[ = e^{3x} \]
So, the solution is given by
\[y \times I . F . = \int Q \times I . F . dx + C\]
\[ \Rightarrow y e^{3x} = \int e^{3x} \times e^{- 2x} dx + C\]
\[ \Rightarrow y e^{3x} = e^x + C\]
\[ \Rightarrow y = e^{- 2x} + C e^{- 3x}\]
APPEARS IN
संबंधित प्रश्न
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`
Solve the differential equation: `x+ydy/dx=sec(x^2+y^2)` Also find the particular solution if x = y = 0.
Find the particular solution of the differential equation `e^xsqrt(1-y^2)dx+y/xdy=0` , given that y=1 when x=0
Find the general solution of the following differential equation :
`(1+y^2)+(x-e^(tan^(-1)y))dy/dx= 0`
Find the particular solution of the differential equation dy/dx=1 + x + y + xy, given that y = 0 when x = 1.
Verify that the given function (explicit or implicit) is a solution of the corresponding differential equation:
y = Ax : xy′ = y (x ≠ 0)
The number of arbitrary constants in the particular solution of a differential equation of third order are ______.
Show that the general solution of the differential equation `dy/dx + (y^2 + y +1)/(x^2 + x + 1) = 0` is given by (x + y + 1) = A (1 - x - y - 2xy), where A is parameter.
Find a particular solution of the differential equation`(x + 1) dy/dx = 2e^(-y) - 1`, given that y = 0 when x = 0.
The solution of the differential equation \[\frac{dy}{dx} + \frac{2y}{x} = 0\] with y(1) = 1 is given by
The solution of the differential equation \[\left( 1 + x^2 \right)\frac{dy}{dx} + 1 + y^2 = 0\], 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 particular solution of the differential equation `(1+y^2)+(x-e^(tan-1 )y)dy/dx=` given that y = 0 when x = 1.
x (e2y − 1) dy + (x2 − 1) ey dx = 0
\[\frac{dy}{dx} + 1 = e^{x + y}\]
`(2ax+x^2)(dy)/(dx)=a^2+2ax`
\[\frac{dy}{dx} + y = 4x\]
`(dy)/(dx)+ y tan x = x^n cos x, n ne− 1`
Find the general solution of the differential equation \[\frac{dy}{dx} = \frac{x + 1}{2 - y}, y \neq 2\]
Solve the following differential equation:-
\[\frac{dy}{dx} + 2y = \sin x\]
Find the equation of a curve passing through the point (0, 1). If the slope of the tangent to the curve at any point (x, y) is equal to the sum of the x-coordinate and the product of the x-coordinate and y-coordinate of that point.
Find the differential equation of all non-horizontal lines in a plane.
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 the differential equation dy = cosx(2 – y cosecx) dx given that y = 2 when x = `pi/2`
Find the general solution of (1 + tany)(dx – dy) + 2xdy = 0.
Find the general solution of `("d"y)/("d"x) -3y = sin2x`
The solution of `("d"y)/("d"x) + y = "e"^-x`, y(0) = 0 is ______.
The solution of the equation (2y – 1)dx – (2x + 3)dy = 0 is ______.
General solution of the differential equation of the type `("d"x)/("d"x) + "P"_1x = "Q"_1` is given by ______.
The solution of differential equation coty dx = xdy is ______.
The integrating factor of `("d"y)/("d"x) + y = (1 + y)/x` is ______.
The member of arbitrary constants in the particulars solution of a differential equation of third order as
Which of the following differential equations has `y = x` as one of its particular solution?
Solve the differential equation:
`(xdy - ydx) ysin(y/x) = (ydx + xdy) xcos(y/x)`.
Find the particular solution satisfying the condition that y = π when x = 1.
