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Method of solution of Exact Differential Equations
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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 F (x, y);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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Method of solution of Exact Differential Equations
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