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Chapter 12: Q. 66 (page 945)

Solve the exact differential equations in Exercises 63鈥�66.12x3y5鈭�15x4y6dydx=0.

Short Answer

Expert verified

The solution of given exact differential equation is:3x4y5+C=0

Step by step solution

01

Step 1. Given information 

Exact differential equation,12x3y5鈭�15x4y6dydx=0

02

Step 2. Solving the given exact differential equation

Given,12x3y5鈭�15x4y6dydx=0鈬�12x3y5dx鈭�15x4y6dy=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�12x3y5dx鈭�鈭�(0)dy=0鈬�12x44y5+C=0鈬�3x4y5+C=0

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Most popular questions from this chapter

Describe the meanings of each of the following mathematical expressions:

fzx0,y0,z0

Describe the meanings of each of the following mathematical expressions:

鈭�f(x,y)

In Exercises 21鈥�26, find the discriminant of the given function.

fx,y=e2xcosy.

Letf(x)beadifferentiablefunctionofx,g(y)beadifferentiablefunctionofy,andh(x,y)=f(x)+g(y).Provethat鈭�2h鈭�x鈭�y=鈭�2h鈭�y鈭�x.

Use Theorem 12.33 to find the indicated derivatives in Exercises 27鈥�30. Express your answers as functions of two variables.

鈭�z鈭�胃whenz=(x2+xy)ey,x=rcos胃andy=rsin胃
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