Advertisements
Advertisements
प्रश्न
Which of the following is a second order differential equation?
पर्याय
(y′)2 + x = y2
y′y′′+ y = sin x
y″ + (y'')2 + y = 0
y′ = y2
उत्तर
y′y′′+ y = sin x
Explanation:
Second-order differential equation is y’y’’+ y = sin x.
APPEARS IN
संबंधित प्रश्न
For the differential equation, find the general solution:
`dy/dx + y/x = x^2`
For the differential equation, find the general solution:
`x dy/dx + 2y= x^2 log x`
For the differential equation, find the general solution:
(1 + x2) dy + 2xy dx = cot x dx (x ≠ 0)
For the differential equation given, find a particular solution satisfying the given condition:
`(1 + x^2)dy/dx + 2xy = 1/(1 + x^2); y = 0` when x = 1
For the differential equation given, find a particular solution satisfying the given condition:
`dy/dx - 3ycotx = sin 2x; y = 2` when `x = pi/2`
Find the general solution of the differential equation `dy/dx - y = sin x`
x dy = (2y + 2x4 + x2) dx
\[\frac{dy}{dx}\] = y tan x − 2 sin x
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`
If f(x) = x + 1, find `"d"/"dx"("fof") ("x")`
Solve the following differential equation:
`("x + a")"dy"/"dx" - 3"y" = ("x + a")^5`
Solve the following differential equation:
`(1 - "x"^2) "dy"/"dx" + "2xy" = "x"(1 - "x"^2)^(1/2)`
`(x + 2y^3 ) dy/dx = y`
The integrating factor of the differential equation (1 + x2)dt = (tan-1 x - t)dx is ______.
The integrating factor of the differential equation `x (dy)/(dx) - y = 2x^2` is
The integrating factor of differential equation `(1 - y)^2 (dx)/(dy) + yx = ay(-1 < y < 1)`
State whether the following statement is true or false.
The integrating factor of the differential equation `(dy)/(dx) + y/x` = x3 is – x.
If y = y(x) is the solution of the differential equation, `(dy)/(dx) + 2ytanx = sinx, y(π/3)` = 0, then the maximum value of the function y (x) over R is equal to ______.
Let y = y(x) be a solution curve of the differential equation (y + 1)tan2xdx + tanxdy + ydx = 0, `x∈(0, π/2)`. If `lim_(x→0^+)` xy(x) = 1, then the value of `y(π/2)` is ______.
Let y = y(x) be the solution curve of the differential equation `(dy)/(dx) + ((2x^2 + 11x + 13)/(x^3 + 6x^2 + 11x + 6)) y = ((x + 3))/(x + 1), x > - 1`, which passes through the point (0, 1). Then y(1) is equal to ______.
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 ______.
If sin x is the integrating factor (IF) of the linear differential equation `dy/dx + Py` = Q then P is ______.
The solution of the differential equation `dx/dt = (xlogx)/t` is ______.
Solve the differential equation `dy/dx+2xy=x` by completing the following activity.
Solution: `dy/dx+2xy=x` ...(1)
This is the linear differential equation of the form `dy/dx +Py =Q,"where"`
`P=square` and Q = x
∴ `I.F. = e^(intPdx)=square`
The solution of (1) is given by
`y.(I.F.)=intQ(I.F.)dx+c=intsquare dx+c`
∴ `ye^(x^2) = square`
This is the general solution.
If sec x + tan x is the integrating factor of `dy/dx + Py` = Q, then value of P is ______.
Solve:
`xsinx dy/dx + (xcosx + sinx)y` = sin x