If Af denotes the space of N times continuously differentiable functions, then the space V of solutions of this differential equation is a subspace of Af.

If the differential equations are nonlinear and have a known solution, it may be possible to linearize the nonlinear differential equations at that solution.

If the resulting linear differential equations have constant coefficients one can take their Laplace transform to obtain a transfer function.

If the weight of the roadway per unit length is w and the weight of the cable and the wire supporting the bridge is negligible in comparison, then the weight on the cable from c to r is wx where x is the horizontal distance between c to r. Proceeding as before gives the differential equation

If one identifies C with R < sup > 2 </ sup >, then the holomorphic functions coincide with those functions of two real variables with continuous first derivatives which solve the Cauchy-Riemann equations, a set of two partial differential equations.

If an inductor is connected to a direct current source with value I via a resistance R, and then the current source is short-circuited, the differential relationship above shows that the current through the inductor will discharge with an exponential decay:

If the fluid being measured is significantly dense, hydrostatic corrections may have to be made for the height between the moving surface of the manometer working fluid and the location where the pressure measurement is desired except when measuring differential pressure of a fluid ( for example across an orifice plate or venturi ), in which case the density ρ should be corrected by subtracting the density of the fluid being measured.

If the string is approximated with 100 discrete mass points one gets the 100 coupled second order differential equations (), () and () or equivalently 200 coupled first order differential equations.

If any two functions are solutions to Laplace's equation ( or any linear homogeneous differential equation ), their sum ( or any linear combination ) is also a solution.

If we define the differential of a function ψ by

If redistribution of wealth via such mechanisms has differential efficiency

If the affine transformation can be decomposed into isometries and a transformation given by a diagonal matrix, we have directionally differential scaling and the diagonal elements ( the eigenvalues ) are the scale factors in two or three perpendicular directions.

If Parkinson's disease has been excluded, the differential diagnosis or list of potential causes for Parkinsonism syndrome includes:

If the Hamiltonian is time-independent, this differential equation can be easily solved to yield

If the dynamics of a system is known, the equations are the solutions to the differential equations describing the motion of the dynamics.

If the patient admits to hair pulling, diagnosis is not difficult ; if patients deny hair pulling, a differential diagnosis must be pursued.

If some of the luminance information arrived via the chrominance channel ( as it would have if RB signals were used instead of differential UV signals ), B & W resolution would have been compromised.

If contains differentiation of, the result will be a differential equation.

If, for example, potential business class customers will pay a large price differential only if economy class seats are uncomfortable while economy class customers are more sensitive to price than comfort, airlines may have substantial incentives to purposely make economy seating uncomfortable.

If the target function is not easily differentiable, the differential with respect to each variable can be approximated as

If the initial and final states are the same, then the integral of an inexact differential may or may not be zero, but the integral of an exact differential will always be zero.

If Acorn had thought to include this small modification in the original Electron design it is likely the machine would have had a much greater impact as it would have nearly doubled the amount of motion possible in games and saved modes 0 – 3 ( including the only 16 colour mode ) from being nearly useless due to contended memory timings.

If a correct signature was located on the cartridge, the 7800 would operate in 7800 mode, granting the game access to MARIA and other features.

If a signature was not located, the 7800 remained in 2600 mode and MARIA was unavailable.

If the < code ><! DOCTYPE html ></ code > declaration is not included, various browsers will revert to " quirks mode " for rendering.

If the player uses the " god mode " cheat from Doom, the game will display a message saying " Trying to cheat, eh?

If the hardware provides multiple rings or CPU modes, the microkernel is the only software executing at the most privileged level ( generally referred to as supervisor or kernel mode ).

( If, in addition, the distribution is unimodal, then the mean = median = mode.

If each mode received an equal partition of energy, the short wavelength modes would consume all the energy.

If the connection to the main controller is interrupted, such readers stop working or function in a degraded mode.

If the main controller fails, sub-controllers change to degraded mode in which doors are either completely locked or unlocked and no events are recorded.

If the extension you call in voice announce mode is not answered, press ITCM before pressing CAMP.

If the terminal driver is in raw mode it no longer interprets control characters, and the EOT character is sent unchanged to the program, which is free to interpret it any way it likes.

If the launch fibre is underfilled, for example as a consequence of being energized by a laser diode or edge-emitting LED, there will be no effect on the mode power distribution or loss measurements.

If the system starts in a particular mode, vibrations in other modes do not develop.

If the annular muscles are contracted, the body cross-section is reduced, and the corresponding segment stretches, since its volume must remain constant due to the incompressible behaviour of the coelom's liquid contents ; this is the usual mode of operation of the hydrostatic skeleton as also employed by other worms.

If the input current is more than, then the SQUID always operates in the resistive mode.

If a block cipher ( not operating in a stream cipher mode ) were to be used in this type of application, the designer would need to choose either transmission efficiency or implementation complexity, since block ciphers cannot directly work on blocks shorter than their block size.

If the player loses, it means that a normal koatari has been hit and the machine enters into jitan mode.

If a mode greater than 24 bits per pixel is desired, the least significant bits are sent on the second link.

If the mode 3 device is unplugged, the switch contacts maintain line connection to the other devices.

If a user has searched, DC ++ will respond with ten search results when the user is in active mode, or five, when the user is in passive mode.

If the wrong codes are entered three times, the game goes into " demo " mode.

If the energy difference between the parent atom and the daughter atom is less than 1. 022 MeV, positron emission is forbidden because not enough decay energy is available to allow it, and thus electron capture is the sole decay mode.