Advertisements
Advertisements
प्रश्न
Solve the differential equation `x dy/dx + y = x cos x + sin x`, given that y = 1 when `x = pi/2`
Advertisements
उत्तर
The given differential equation is
`x dy/dx + y = x cos x + sin x`
`=> dy/dx + y/x = (x cos x + sin x)/x`
This is a linear differential equation of the form `dy/dx + Py = Q`
Thus, the particular solution of the given differential equation is y = sinx.
संबंधित प्रश्न
For the differential equation, find the general solution:
`dy/dx + y/x = x^2`
The integrating factor of the differential equation.
`(1 - y^2) dx/dy + yx = ay(-1 < y < 1)` is ______.
The population of a village increases continuously at the rate proportional to the number of its inhabitants present at any time. If the population of the village was 20000 in 1999 and 25000 in the year 2004, what will be the population of the village in 2009?
Solve the differential equation `(tan^(-1) x- y) dx = (1 + x^2) dy`
Find the general solution of the differential equation `dy/dx - y = sin x`
(x + tan y) dy = sin 2y dx
\[\frac{dy}{dx}\] + y cos x = sin x cos x
Solve the differential equation \[\left( y + 3 x^2 \right)\frac{dx}{dy} = x\]
Find the particular solution of the differential equation \[\frac{dx}{dy} + x \cot y = 2y + y^2 \cot y, y ≠ 0\] given that x = 0 when \[y = \frac{\pi}{2}\].
Solve the following differential equation:- \[\left( \cot^{- 1} y + x \right) dy = \left( 1 + y^2 \right) dx\]
Solve the following differential equation: \[\left( \cot^{- 1} y + x \right) dy = \left( 1 + y^2 \right) dx\] .
Find the integerating factor of the differential equation `x(dy)/(dx) - 2y = 2x^2`
Find the integerating factor of the differential equation `xdy/dx - 2y = 2x^2` .
Solve the differential equation: (1 +x2 ) dy + 2xy dx = cot x dx
Solve the following differential equation:
`("x + a")"dy"/"dx" - 3"y" = ("x + a")^5`
Solve the following differential equation:
dr + (2r cotθ + sin2θ)dθ = 0
Solve the following differential equation:
`(1 - "x"^2) "dy"/"dx" + "2xy" = "x"(1 - "x"^2)^(1/2)`
Form the differential equation of all circles which pass through the origin and whose centers lie on X-axis.
The slope of the tangent to the curves x = 4t3 + 5, y = t2 - 3 at t = 1 is ______
Integrating factor of the differential equation `(1 - x^2) ("d"y)/("d"x) - xy` = 1 is ______.
The integrating factor of differential equation `(1 - y)^2 (dx)/(dy) + yx = ay(-1 < y < 1)`
If the solution curve y = y(x) of the differential equation y2dx + (x2 – xy + y2)dy = 0, which passes through the point (1, 1) and intersects the line y = `sqrt(3) x` at the point `(α, sqrt(3) α)`, then value of `log_e (sqrt(3)α)` is equal to ______.
Find the general solution of the differential equation:
`(x^2 + 1) dy/dx + 2xy = sqrt(x^2 + 4)`
If sec x + tan x is the integrating factor of `dy/dx + Py` = Q, then value of P is ______.
