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Chapter 12: Q. 64 (page 945)

Solve the exact differential equations in Exercises 63鈥�66.ycos(xy)鈭�3+(xcos(xy)+2)dydx=0.

Short Answer

Expert verified

The solution of given exact differential equation is:sin(xy)-3x+2y+C=0

Step by step solution

01

Step 1. Given information 

Exact differential equation,ycos(xy)鈭�3+(xcos(xy)+2)dydx=0

02

Step 2. Solving the given exact differential equation

ycos(xy)鈭�3+(xcos(xy)+2)dydx=0鈬�ycos(xy)鈭�3dx+(xcos(xy)+2)dy=0ItisaexactdifferentialequationofthetheformMdx+Ndy=0,with鈭�M鈭�y=鈭�N鈭�x.thesolutionisgivenby,f(x,y)=鈭�(treatingyasconstantinM)dx+鈭�(termsindependentofxinN)dy=0鈬�鈭�ycos(xy)鈭�3dx+鈭�(2)dy=0鈬�sin(xy)-3x+2y+C=0

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