Solution of Differential Equations well explained
SOLUTION OF DIFFERENTIAL EQUATIONS
A differential equation is an equation that relates a function to its derivatives.
In simpler terms, it's an equation that tells you something about how a function changes.
Finding the solution to a differential equation means finding a function that satisfies the equation.
There are two main types of solutions:
1. General solution: This solution contains arbitrary constants, which can be adjusted to fit specific situations. The number of arbitrary constants is equal to the order of the differential equation.
2. Particular solution: This solution is obtained by applying specific values to the arbitrary constants in the general solution.
It satisfies the differential equation and also meets certain initial or boundary conditions.
For example: dy/dx = 5
is a differential equation
The solution is: y=5x+c
which is the general solution for the equation of a straight line with gradient 5.
If the data includes the fact that when y=2 when x=-1 then the constant will be determined as:
2=5(-1)+c
2+5=c
c=7
Substituting c=7 into the general solution
y=5x+c. gives:
y=5x+7
Which is the particular solution.