Tuesday, December 16, 2014

Solve the differential equation.

An ordinary differential equation (ODE)  is differential equation for the derivative of a function of one variable. When an ODE is in a form of , this is just a first order ordinary differential equation. 


The given problem: is in a form of .


 To evaluate this, we may express as .


 The problem becomes:



We may apply the variable separable differential equation: x.


Cross-multiply to the right side:



Cross-multiply to the left side:



Apply direct integration on both sides:



Apply basic integration property:  on both sides:



For the left side, we apply the Power Rule for integration: .



               


               



For the right side, we apply Law of Exponent: before applying the Power Rule for integration: .



                       


                       


                       



Combining the results, we get the general solution for differential equation:



We may simplify it as:





 

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