Register to reply

Variable substitution question(diff)

Share this thread:
Aug16-09, 04:12 PM
P: 5
[tex]\frac{xy'}{(\ln x\arctan y)-1}=(1+y^2)\arctan y\\[/tex]
[tex]t=\arctan y\\[/tex]
[tex]\frac{x}{\ln (x)t-1}=\frac{t}{t'}\\[/tex]

[tex]\frac{x}{\ln (x)t-1}=\frac{tdx}{dt}\\[/tex]
[tex]xdt=(\ln (x)t-1)tdx\\[/tex]
[tex]\frac{dt}{\ln (x)t-1}=\frac{dx}{x}\\[/tex]
still cant beak it as one type of variable on each side
so i substitute by another variable
[tex]z=\ln x\\[/tex]
i dont know how to separate each variable type on one side
so i could integrate

Phys.Org News Partner Science news on
'Smart material' chin strap harvests energy from chewing
King Richard III died painfully on battlefield
Capturing ancient Maya sites from both a rat's and a 'bat's eye view'
Aug19-09, 06:50 PM
P: 355
First of all, your last substitution should result in
I'm not exactly sure on a good substitution to use, but since this is a Bernoulli ODE, you can use that method.

Register to reply

Related Discussions
How to know here on what variable its a derivative of..(diff) Calculus & Beyond Homework 5
Variable substitution problem Calculus & Beyond Homework 3
V substitution in homogeneous equations (diff eq) Calculus & Beyond Homework 2
Question on substitution Calculus & Beyond Homework 2
Cant solve diff-eq with substitution Introductory Physics Homework 4