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Chapter 12: Q. 65 (page 945)

Solve the exact differential equations in Exercises 63鈥�66.exlny+x3+exydydx=0

Short Answer

Expert verified

The solution of given exact differential equation is:exlny+x44+C=0

Step by step solution

01

Step 1. Given information

Exact differential equation,exlny+x3+exydydx=0

02

Step 2. Solving the given exact differential equation

Given,exlny+x3+exydydx=0鈬�exlny+x3dx+exydy=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�exlny+x3dx+鈭�(0)dy=0鈬�exlny+x44+C=0

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