What is the particular solution to the differential equation?
A solution yp(x) of a differential equation that contains no arbitrary constants is called a particular solution to the equation.
What is a complementary 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.
How do you calculate undetermined coefficients?
The central idea of the method of undetermined coefficients is this: Form the most general linear combination of the functions in the family of the nonhomogeneous term d( x), substitute this expression into the given nonhomogeneous differential equation, and solve for the coefficients of the linear combination.
What is meant by particular solution?
: the solution of a differential equation obtained by assigning particular values to the arbitrary constants in the general solution.
What is general and particular solution?
General Solution of a Differential Equation When the arbitrary constant of the general solution takes some unique value, then the solution becomes the particular solution of the equation.
What is the difference between general solution and particular solution?
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 are the particular and total solution?
The total solution or the general solution of a non-homogeneous linear difference equation with constant coefficients is the sum of the homogeneous solution and a particular solution. If no initial conditions are given, obtain n linear equations in n unknowns and solve them, if possible to get total solutions.
What is the general solution?
1 : a solution of an ordinary differential equation of order n that involves exactly n essential arbitrary constants. — called also complete solution, general integral. 2 : a solution of a partial differential equation that involves arbitrary functions. — called also general integral.
What are the disadvantages of method of undetermined coefficients?
Pros and Cons of the Method of Undetermined Coefficients:The method is very easy to perform. However, the limitation of the method of undetermined coefficients is that the non-homogeneous term can only contain simple functions such as , , , and so the trial function can be effectively guessed.