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How do I find a particular solution by inspection?

Solving by inspection simply means you look at the problem, and try to come up with a solution through trial and error, using some logical thinking. In this case, setting y=5 is a solution to the equation. Since the RHS of y″+2y=10 is a constant, you try y=C in your equation.

What is the best method to solve initial value problem?

Some implicit methods have such good stability properties that they can solve stiff initial value problems with step sizes that are appropriate to the behavior of the solution if they are evaluated in a suitable way. The backward Euler method and the trapezoidal rule are examples.

What is an example of steady state?

One of the simplest examples of such a system is the case of a bathtub with the tap open but without the bottom plug: after a certain time the water flows in and out at the same rate, so the water level (the state variable being Volume) stabilizes and the system is at steady state.

What is the difference between steady-state and unsteady state?

Steady-state and unsteady-state processes describe the time interval that a process occurs over. Steady-state refers to the time where the variable of interest doesn’t change. Unsteady-state is when the variable of interest changes over time.

What is unsteady state heat transfer?

If the temperature of a body does not vary with time, it is said to be in steady state. During this period, the temperature varies with time and body is said to be in the unsteady or transient state. This phenomenon is known as Unsteady or transient heat conduction.

What is unsteady state diffusion?

Unsteady state diffusion or non-steady state diffusion is a form of diffusion in which the rate of diffusion is a function of time. This means the rate of diffusion is time-dependent. Therefore, the rate of the concentration with distance (dc/dx) is not a constant and the change of concentration with time is not zero.

What is non steady flow?

A steady flow is one in which the conditions of velocity, pressure, and cross–section may differ from point to point but do not change with time. If at any point in the fluid, the conditions change with time, the flow is described as unsteady.

What is steady flow process and unsteady flow process?

In a steady flow process we have assumed that the mass and energy within the system remain constant and do not vary with time. In an unsteady flow process, mass and energy within the control volume vary continuously. The fluid flow into and out of the system.

What fluid flow is laminar?

Laminar flow or streamline flow in pipes (or tubes) occurs when a fluid flows in parallel layers, with no disruption between the layers. At low velocities, the fluid tends to flow without lateral mixing, and adjacent layers slide past one another like playing cards.