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Stuck with integration of differential equation by seperation of variables

  • Thread starter dooogle
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  • #1
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Homework Statement



dy/dx=-ylny/x initial conditions y(x=1)=1

express answer in the form f(x,y)=0

Homework Equations



The Attempt at a Solution



i let u=ln y

du/dy=1/y

y*du=dy

subbing into equation gives int(y/yu du)=-int dx

which is equal to int(1/u du)=-int(1/x) dx

ln (u)=-ln (x) +c

subbing back in for u gives ln(ln (y))=-ln (x)+c

ln (y)=1/x +c

when x= 1 y=1

ln(1)=1/1 +c

0=1+c

c=-1

equation becomes ln(ln(y))=-ln(x)+c

rearranging (here im concerned that i make a mistake but im not sure)

ln(ln(y))+ln(x)+1=0

thank you for your time

dooogle
 

Answers and Replies

  • #2
vela
Staff Emeritus
Science Advisor
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Education Advisor
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It looks like you used c to mean two different things near the end. You need to fix that.

You could solve for y explicitly in terms of x and plug that back into the original equation to verify it's a solution.
 

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