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Order and degree of a differential equation
The order of a DE is the order of the highest ordered derivative involved in the expression. The degree of the an ordinary differential equation is the algebraic degree of its highest ordered–derivative.
Example 3: 
is first order, first degree ordinary DE
Example 4: 
is first order, first degree partial DE
Example 5: 
is second order, first degree ordinary DE
We say that a function is a solution to a differential equation if, when we plug it (and its various derivatives) into the equation, we find that the equation is satisfied.
Our use of the word solution has been until now somewhat informal. To be precise, we say that the continuous function 
is a solution of the differential equation in
on the interval I provided that the derivatives 
exist on I and
for all x in I. For the sake of brevity, we may say that satisfies the differential equation in on I.
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