Solving Linear ODEs Using Maples dsolve Command

Solving Linear ODEs Using Maple s dsolve Command... 

In the previous sections we solved linear ODEs using exponential matrix (section 2.1.2 - 2.1.4) and the Laplace transform technique (section 2.1.5). Alternatively, Maple s dsolve command can be used to solve linear ODEs. However, the analytical solution obtained from the dsolve command may not be in a simplified form. 

Higher order linear ODEs can also be solved using the dsolve command. It should be noted that Maple solves equations in symbolic form. Therefore, even if the constants are numerical, the output is in symbolic form. Sometimes, this output can be messy. It should be noted that when more than two equations are solved the dsolve command may not be able to give an elegant solution. For illustration, the heat transfer problem solved in example 2.3 is solved below using Maple s dsolve command. 

Maple s dsolve command was used to solve linear ODEs in section 2.1.6. In our opinion, exponential matrix method is the best method to arrive at an elegant analytical solution. The Laplace transform technique illustrated in section 2.1.5 could be used for integro-differential equations. Maple s dsolve command has to be used if the exponential matrix method fails. 

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