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In this post, we define Solution of a Differential Equation, General Solutions, Particular Solution, Equations with Separable Variables and also Linear Equations.
Solution of a Differential Equation
It is a relation between variables not involving differential coefficients such that this relation and the derivatives obtained from it satisfy the given differential equation.
General Solutions:
A solution of a differential equation called general solution which contains arbitrary constants as many as the order of the differential equation.
Particular Solution
A solution obtained by giving particular values to the arbitrary constants in the general solution is called particular solution.
Equations with Separable Variables
If we put the differential equation in the form f(x) dx +¢(y) dy =0, then it is called
variable separable. Now It is very easy to get the solution of it by integrating it and adding one constant on any side.
f(x) dx +¢(y) dy =0
∫f(x) dx +∫¢(y) dy =constant
Linear Equations:
A differential equation of the form
dy/dx +Py=Q
Where P and Q are functions of x but not y is called linear differential equation of first order. In the same way,
A differential equation of the form dx/dy +Py=Q
Where P and Q are functions of y but not x is called linear differential equation of first order.
Read related definitions: Click Here
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