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Method of solution of Exact Differential Equations


Method of solution of Exact Differential Equations 


If the given equation is exact then the solution procedure consists of the following steps:
Step 1. Check that the equation is exact by verifying the condition  
Step 2. Write down the system 
Step 3. Integrate either the 1st equation w. r. to x or 2nd w. r. to y. If we choose the 1st equation then
                                                     
   The function is an arbitrary function of , integration w.r.to  being constant.
Step 4. Use second equation in step 2 and the equation in step 3 to find .
                                               
                                               
Step 5. Integrate to find  and write down the function (xy);
Step 6. All the solutions are given by the implicit equation
                                                             
Step 7. If you are given an IVP, plug in the initial condition to find the constant C.
Caution: should disappear from. Otherwise something is wrong!        

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