Advertisements
Advertisements
प्रश्न
Correct substitution for the solution of the differential equation of the type `("d"y)/("d"x) = "f"(x, y)`, where f(x, y) is a homogeneous function of zero degree is y = vx.
पर्याय
True
False
उत्तर
This statement is True.
Explanation:
Since particular solution of a differential equation has no arbitrary constant.
APPEARS IN
संबंधित प्रश्न
Solve the following differential equation: `(x^2-1)dy/dx+2xy=2/(x^2-1)`
Find the integrating factor of the differential equation.
`((e^(-2^sqrtx))/sqrtx-y/sqrtx)dy/dx=1`
Solve the differential equation `sin^(-1) (dy/dx) = x + y`
The decay rate of radium at any time t is proportional to its mass at that time. Find the time when the mass will be halved of its initial mass.
A wet porous substance in the open air loses its moisture at a rate proportional to the moisture content. If a sheet hung in the wind loses half of its moisture during the first hour, when will it have lost 95% moisture, weather conditions remaining the same.
Solve the differential equation: (x + 1) dy – 2xy dx = 0
`("e"^(-2sqrt(x))/sqrt(x) - y/sqrt(x))("d"x)/("d"y) = 1(x ≠ 0)` when written in the form `"dy"/"dx" + "P"y` = Q, then P = ______.
`"dy"/"dx" + y` = 5 is a differential equation of the type `"dy"/"dx" + "P"y` = Q but it can be solved using variable separable method also.
If α, β are different values of x satisfying the equation a cos x + b sinα x = c, where a, b and c are constants, then `tan ((alpha + beta)/2)` is
The solution of the differential equation `(dy)/(dx) = 1 + x + y + xy` when y = 0 at x = – 1 is
`int cos(log x) dx = F(x) + C` where C is arbitrary constant. Here F(x) =
Form the differential equation of the family of parabolas having vertex at origin and axis along positive y-axis.
Solve the differential equation: xdy – ydx = `sqrt(x^2 + y^2)dx`
Solve the following differential equation: (y – sin2x)dx + tanx dy = 0
Find the general solution of the differential equation: (x3 + y3)dy = x2ydx
If y = y(x) is the solution of the differential equation `(1 + e^(2x))(dy)/(dx) + 2(1 + y^2)e^x` = 0 and y(0) = 0, then `6(y^'(0) + (y(log_esqrt(3))))^2` is equal to ______.
Let y = y(x) be the solution of the differential equation, `(2 + sinxdy)/(y + 1) (dy)/(dx)` = –cosx. If y > 0, y(0) = 1. If y(π) = a, and `(dy)/(dx)` at x = π is b, then the ordered pair (a, b) is equal to ______.
The solution of the differential equation `(1 + y^2) + (x - e^(tan^-1y)) (dy)/(dx)` = 0, is ______.