Question

Could you give me an example of the difference between ODEs and PDEs? We got stuck with a terrible Diff Eqns book that uses no examples.

Answer 1

This is ODE, only one variable
y(x)=y′(x)

solution

y(x)= Ce^x

y(x,y)=yx′(x,y)


solution
y(x,y)= f(y )e^x

Answer 2

This is ODE, only one variable
y(x)=y′(x)

solution
y(x)= Ce^x

This is PDE;more than one variable
\[y(x,y)=y_x′(x,y)\]

solution
y(x,y)= f(y )e^x

Answer 3

@imranmeah91 is correct.
You may interested in these online references on these topics:
1) http://homepage.mac.com/nshoffner/nsh/ODE/Def_Class.html
2) http://tutorial.math.lamar.edu/Classes/DE/Definitions.aspx

Answer 4

@imranmeah91, so the ODE would be written out as dy/dx, while the PDE might be written as y(d/dx)?