Partial differential equations are mathematical equations that involve two or more independent variables, an unknown function, and partial derivatives of the unknown function. Even the explanation is confusing! If, however, anyone chooses to learn about PDE there are classes offered at any institution of higher learning.
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ordinary differential equation is obtained only one independent variable and partial differential equation is obtained more than one variable.
The answer will depend very much on the nature of the equation. The steps required for a one-step equation are very different from the steps required for a partial differential equation. For some equations there are no straightforward analytical methods of solution: only numerical methods.
Differential equations were invented separately by Isaac Newton and Gottfried Leibniz. This debate on who was the first one to invent it was argued by both Isaac and Gottfried until their death.
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There are plenty of places in order for one to learn more about algorithmic equations. However, one might want to check out brief information about algorithmic equations on the website Wikipedia.