Advertisements
Advertisements
प्रश्न
State whether the following statement is true or false.
The integrating factor of the differential equation `(dy)/(dx) + y/x` = x3 is – x.
पर्याय
True
False
उत्तर
This statement is False.
Explanation:
`(dy)/(dx) + y/x` = x3
∴ `(dy)/(dx) + (x^-1). y = x^3`
Comparing with `(dy)/(dx) + Py = Q`, we get
P = x–1, Q = x3
Now, I.F. = `e^(intpdx)`
= `e^(intx^-1 dx)`
= `e^(logx)`
= x.
APPEARS IN
संबंधित प्रश्न
For the differential equation, find the general solution:
`x dy/dx + y - x + xy cot x = 0(x != 0)`
For the differential equation given, find a particular solution satisfying the given condition:
`dy/dx + 2y tan x = sin x; y = 0 " when x " = pi/3`
For the differential equation given, find a particular solution satisfying the given condition:
`dy/dx - 3ycotx = sin 2x; y = 2` when `x = pi/2`
The Integrating Factor of the differential equation `dy/dx - y = 2x^2` is ______.
Find the general solution of the differential equation `dy/dx - y = sin x`
Find the general solution of the differential equation \[x\frac{dy}{dx} + 2y = x^2\]
Solve the following differential equation:-
\[\left( 1 + x^2 \right)\frac{dy}{dx} - 2xy = \left( x^2 + 2 \right)\left( x^2 + 1 \right)\]
Find the integerating factor of the differential equation `xdy/dx - 2y = 2x^2` .
Solve the differential equation: `(1 + x^2) dy/dx + 2xy - 4x^2 = 0,` subject to the initial condition y(0) = 0.
Solve the following differential equation:
`"x" "dy"/"dx" + "2y" = "x"^2 * log "x"`
Solve the following differential equation:
`("x + y") "dy"/"dx" = 1`
Solve the following differential equation:
`("x + a")"dy"/"dx" - 3"y" = ("x + a")^5`
Solve the following differential equation dr + (2r cot θ + sin 2θ) dθ = 0.
Solve the following differential equation:
y dx + (x - y2) dy = 0
Find the equation of the curve which passes through the origin and has the slope x + 3y - 1 at any point (x, y) on it.
Integrating factor of the differential equation `(1 - x^2) ("d"y)/("d"x) - xy` = 1 is ______.
The solution of `(1 + x^2) ("d"y)/("d"x) + 2xy - 4x^2` = 0 is ______.
The equation x2 + yx2 + x + y = 0 represents
Let y = f(x) be a real-valued differentiable function on R (the set of all real numbers) such that f(1) = 1. If f(x) satisfies xf'(x) = x2 + f(x) – 2, then the area bounded by f(x) with x-axis between ordinates x = 0 and x = 3 is equal to ______.
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 ______.
The solution of the differential equation `dx/dt = (xlogx)/t` is ______.
The slope of tangent at any point on the curve is 3. lf the curve passes through (1, 1), then the equation of curve is ______.
Solve:
`xsinx dy/dx + (xcosx + sinx)y` = sin x
The slope of the tangent to the curve x = sin θ and y = cos 2θ at θ = `π/6` is ______.
