Sentence examples for constant of integration from inspiring English sources

and by using the wave variable η = x − ct reduces it to an ODE − c + 3 2 v + 2 v 3 + v ′ ′ = 0, Open image in new window (3.6). in which Equation 3.6 is obtained by integrating and neglecting the constant of integration.

and by using the wave variable η = x + y − ct reduces it to an ODE − c − 5 2 v − 2 v 3 + v ′′ = 0, Open image in new window (4.27). in which Equation 4.27 is obtained by integrating and neglecting the constant of integration.

Using the wave variable ξ = x − vt converts Eq. (31) to an ODE vu+u^3+avu^{primeprime}=0, (32 which is obtained after integrating once and setting the constant of integration to zero.

Using the wave variable ξ = x − V t in (19) then integrating this equation and considering the constant of integration to be zero, we obtain ( − V + γ ) U − α U ′ + θ 2 U 2 + ( V + β ) U ′ ′ = 0. (20..

Case 2. g ( u ) = u 2 2. Using the wave variable ξ = x − V t, then by integrating this equation and considering the constant of integration to be zero, we obtain ( V − β ) U − V U ′ ′ + α U ′ + 1 2 U 2 = 0. (25).

We will investigate the equation for λ ≠ 0 and α ∈ R. Using the wave variable ξ = x − V t in (31) then integrating this equation and considering the constant of integration to be zero, we obtain − V U + λ U ′ ′ − α U ′ + 1 2 U 2 = 0. (32).

* There are other possible solutions involving so-called "constants of integration".

Several pieces of information about the governing differential equation on the stencil are incorporated into the IRBF approximations by means of the constants of integration.

A linear combination of these solutions specifies the general acoustic field; the constants of integration are determined from boundary conditions of which several examples are given.

(64 where (C 5) and (C 6) are constants of integration.

where C 1, C 2, and C 3 are constants of integration to be determined.