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 general solution of differential equation?
A solution of a differential equation is an expression for the dependent variable in terms of the independent one(s) which satisfies the relation. The general solution includes
all possible solutions
and typically includes arbitrary constants (in the case of an ODE) or arbitrary functions (in the case of a PDE.)
What is general and particular solution?
By using the boundary conditions (also known as the initial conditions) the particular solution of a differential equation is obtained. So, to obtain a particular solution, first of all, a general solution
is found out
and then, by using the given conditions the particular solution is generated.
What do you mean by general solution and 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 the difference between general and particular solution of 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 does General solution mean?
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.
Why is Euler’s method used?
Euler’s method is a
numerical method that you can use to approximate the solution to an initial value problem with a differential equation
that can’t be solved using a more traditional method, like the methods we use to solve separable, exact, or linear differential equations.
What is general solution in trigonometry?
Solutions for Trigonometric Equations. … are solutions of the given equation. Hence, the general solution for sin x = 0 will be,
x = nπ, where n∈I
. Similarly, general solution for cos x = 0 will be x = (2n+1)π/2, n∈I, as cos x has a value equal to 0 at π/2, 3π/2, 5π/2, -7π/2, -11π/2 etc.
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.
How do you find the general solution?
So the general solution to the differential equation is found by integrating IQ and then re-arranging the formula to make y the subject. x3 dy dx + 3x2y = ex so integrating both sides we have x3y = ex + c where c is a constant. Thus the general solution is
y = ex + c x3
.
What is particular to general?
As adjectives the difference between particular and general
is that particular is (obsolete)
pertaining only to a part of something
; partial while general is including or involving every part or member of a given or implied entity, whole etc; as opposed to (specific) or (particular).
What is a particular equation?
: the solution of a differential equation obtained by assigning particular values to the arbitrary constants in the general solution.
What is the general solution in maths?
The general solution (EMCGJ)
The periodicity of the trigonometric functions means that
there are an infinite number of positive and negative angles that satisfy an equation
. If we do not restrict the solution, then we need to determine the general solution to the equation.
