I understand the two terms as follows: Homogenous solution – if x + y = b, then any ax + ay = b is also true, for any real number, except perhaps zero (if b is nonzero). Particular solution – any specific solution to the system.

What is homogeneous and particular solution?

I understand the two terms as follows: Homogenous solution – if x + y = b, then any ax + ay = b is also true, for any real number, except perhaps zero (if b is nonzero). Particular solution – any specific solution to the system.

What is homogeneous de?

A homogeneous differential equation is an equation containing a differentiation and a function, with a set of variables. The function f(x, y) in a homogeneous differential equation is a homogeneous function such that f(λx, λy) = λnf(x, y), for any non zero constant λ.

What is particular solution?

Definition of particular solution : the solution of a differential equation obtained by assigning particular values to the arbitrary constants in the general solution.

What is heterogeneous solution?

Heterogeneous solutions are solutions with non-uniform composition and properties throughout the solution. A solution of oil and water, water and chalk powder and solution of water and sand, etc.

Can a homogeneous system have a unique solution?

Since a homogeneous system always has a solution (the trivial solution), it can never be inconsistent. Thus a homogeneous system of equations always either has a unique solution or an infinite number of solutions.

What is difference between homogeneous and nonhomogeneous equation?

For a homogeneous system of linear equations either (1) the system has only one solution, the trivial one; (2) the system has more than one solution. For a non-homogeneous system either (1) the system has a single (unique) solution; (2) the system has more than one solution; (3) the system has no solution at all.

What is the difference between particular and general solution?

So here is the explanation. Particular solution is just a solution that satisfies the full ODE; general solution on the other hand is complete solution of a given ODE, which is the sum of complimentary solution and particular solution.

What is general and particular solution?

A particular solution of differential equation is a solution of the form y = f(x), which do not have any arbitrary constants. The general solution of the differential equation is of the form y = f(x) or y = ax + b and it has a, b as its arbitrary constants.

What is homogeneous vs heterogeneous?

There are two types of mixtures: heterogeneous and homogeneous. Heterogeneous mixtures have visually distinguishable components, while homogeneous mixtures appear uniform throughout. The most common type of homogenous mixture is a solution, which can be a solid, liquid, or gas. Created by Sal Khan.

What is the difference between homogeneous and heterogeneous solution?

A homogenous mixture is that mixture in which the components mix with each other and its composition is uniform throughout the solution. A heterogenous mixture is that mixture in which the composition is not uniform throughout and different components are observed.

What does nontrivial solution mean?

A solution or example that is not trivial. Often, solutions or examples involving the number zero are considered trivial. Nonzero solutions or examples are considered nontrivial. For example, the equation x + 5y = 0 has the trivial solution (0, 0).

What is difference between trivial and nontrivial solution?

Since the zero solution is the “obvious” solution, hence it is called a trivial solution. Any solution which has at least one component non-zero (thereby making it a non-obvious solution) is termed as a “non-trivial” solution.

What is complementary and particular solution?

Solution of the nonhomogeneous linear equations The term yc = C1 y1 + C2 y2 is called the complementary solution (or the homogeneous solution) of the nonhomogeneous equation. The term Y is called the particular solution (or the nonhomogeneous solution) of the same equation.

What is homogeneous solution?

Homogeneous solutions are solutions with uniform composition and properties throughout the solution. For example a cup of coffee, perfume, cough syrup, a solution of salt or sugar in water, etc. Heterogeneous solutions are solutions with non-uniform composition and properties throughout the solution.

Is solution a homogeneous mixture?

Solution: a homogeneous mixture of two or more substances. Example: water, sugar, flavor mixture (Coke). The substances are physically combined, not chemically combined or bonded to each other. Solvent: usually the substance in the greater amount.

Are all solutions homogeneous mixtures?

“Solution” always implies mixing on the molecular level (single-phase). To summarize: Solutions are always homogeneous mixtures, but homogeneous mixtures are not always solutions.

What is nontrivial solution in homogeneous system?

Any solution in which at least one variable has a nonzero value is called a nontrivial solution.

What is homogeneous and non-homogeneous linear equation?

There may be two types of linear equations, homogeneous and nonhomogeneous. A homogeneous equation does have zero on the right hand side of the equality sign, while a non-homogeneous equation has a function of independent variable on the right hand side of the equal sign.