Table of Contents
- 1 What is the difference between a general solution and a particular solution of a differential equation?
- 2 What are particular solutions where do they come from and what is their relation to a general solution?
- 3 What is complementary and particular solution?
- 4 What is a complementary solution?
- 5 What is the particular solution of a differential equation?
- 6 What are the complementary and particular solutions of linear differential equations?
What is the difference between a general solution and a particular solution of a differential equation?
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 particular solutions where do they come from and what is their relation to a general solution?
If the number of arbitrary constants in the solution is equal to the order of the differential equation, the solution is called as the general solution. If the arbitrary constants in the general solution are given particular values, the solution is called a particular solution (of the differential equation).
What is difference between particular solution and singular solution?
Singular solution: The equation of the envelope of the surface represented by the complete integral of a pde is called singular solution. It differs from particular solution in the sense that it cannot be, in general, be obtained from the complete integral by giving particular values to the arbitrary constants.
Why is it important to solve the particular solution of a differential equation?
Particular Solution of a Differential Equation The conditions for calculating the values of the arbitrary constants can be provided to us in the form of an Initial-Value Problem, or Boundary Conditions, depending on the problem.
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 a complementary solution?
homogeneous equation. y″ + p(t)y′ + q(t)y = 0. (That is, y1 and y2 are a pair of fundamental solutions of the corresponding homogeneous equation; C1 and C2 are arbitrary constants.) The term yc = C1 y1 + C2 y2 is called the complementary solution (or the homogeneous solution) of the nonhomogeneous equation.
What is particular solution of a differential equation?
A Particular Solution of a differential equation is a solution obtained from the General Solution by assigning specific values to the arbitrary constants.
What is complementary function in partial differential equation?
The solution which contains a number of arbitrary constants equal to the order of the differential equation is called the complementary function (C.F.) of a Differential equation. ❖ Auxiliary Equation: An equation f (D,D’) = 0 is Auxiliary Equation . ❖
What is the particular solution of a differential equation?
Particular Solution of a Differential Equation. A Particular Solution of a differential equation is a solution obtained from the General Solution by assigning specific values to the arbitrary constants.
What are the complementary and particular solutions of linear differential equations?
The complementary and particular solutions are two easy find (and sufficient) linearly independent ones. In my textbooks, the complementary solution was called the homogenous solution, and I’ll use that. The general solution to a linear differential equation is the sum of linearly independent solutions.
What is the difference between complimentary solution and general 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. Thanks for contributing an answer to Mathematics Stack Exchange!
Why do we say “a particular solution” instead of the particular solution?
Notice in the last example that we kept saying “a” particular solution, not “the” particular solution. This is because there are other possibilities out there for the particular solution we’ve just managed to find one of them. Any of them will work when it comes to writing down the general solution to the differential equation. Speaking of which…