Differential Equation Significance If y=mx+c is an equation that can be represented on a graph paper by a Straight Line. 
I was curious to know how would you represent a differential equation on Graph.


*

*Partial Differential Equation 

*Ordinary differential Equation


Again . if we Solve two Straight line equations . We get a point if the lines intersect which we can very easily see and plot on graph. I would like to know what we get when we solve differential equations and how do we represent it on graph. 
 A: There is a fundamental difference in the types of equations you mention.
Solutions of the first type of equation, which can be written with more generality as $$f(x,y)=0,$$
are pairs of numbers (assuming you intend real variables here). "Graphing" the set of all such solutions is possible in the way you mention because pairs of real numbers correspond to points in the plane, so it is theoretically simple to highlight with pencil such points on a piece of graph paper representing the plane. Your equation $y=mx+c$ corresponds to the equation $f(x,y)=0$ where the function $f:\mathbb R\to \mathbb R$ has the rule $f(x,y)=mx+c-y$.
Differential equations are another matter. Solutions to the first type of equation are points, but solutions to differential equations are functions. I can't address every possible type of DE here, but one often seeks a function $y=f(x)$ satisfying some DE. In the absence of additional constraints, there are typically many solutions. So now, instead of plotting a bunch of individual points, you would plot a bunch of individual functions.
It would be important to distinguish them instead of just highlighting the points in the plane on the collection of graphs, because they could span a region. The individual curves are of interest.
