Saturday, September 14, 2013

Find the general solution of the differential equation

The general solution of a differential equation in a form of can


 be evaluated using direct integration. The derivative of y denoted as can be written as then can be expressed as .


For the problem , we may apply to set-up the integration:


.


 or



 Then set-up direct integration on both sides:



Integration:


Apply Power Rule integration: on  .


Note: is the same as .



           


Apply the basic integration property:  and basic integration formula for sine function:



                   



 Then combining the results for the general solution of differential equation:





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