Can anyone check if my answer for this ODE is correct?

  • Thread starter ronaldor9
  • Start date
  • #1
92
1

Homework Statement


[tex](x+2y-4)\,dx - (2x-4y)\,dy=0[/tex]




The Attempt at a Solution


My answer,
[tex]\mathrm{ln}[4(y-1)^2+(x-2)^2] + 2\mathrm{arctan}\frac{x-2}{2y-2}=C[/tex]
Textbook's answer,
[tex]\mathrm{ln}[4(y-1)^2+(x-2)^2] - 2\mathrm{arctan}\frac{2y-2}{x-2}=C[/tex]
 
Last edited:

Answers and Replies

  • #2
tiny-tim
Science Advisor
Homework Helper
25,832
251
Hi ronaldor9! :smile:

tan(a) = 1/tan(π/2 - a), so theyr'e the same, except for a constant :wink:

what were the initial conditions?
 
  • #3
92
1
Hey, sorry i meant to place a constant instead of the zero.
Does that identity work for arctan?
 
  • #4
tiny-tim
Science Advisor
Homework Helper
25,832
251
Hey, sorry i meant to place a constant instead of the zero.
Does that identity work for arctan?
oh come on

if tan(a) = 1/tan(π/2 - a),

then putting T = tan(a) gives 1/T = tan(π/2 - a),

so arctanT = a = π/2 - arctan(1/T)
 
  • #5
92
1
Thanks! tiny-tim
 

Related Threads on Can anyone check if my answer for this ODE is correct?

Replies
2
Views
815
  • Last Post
Replies
5
Views
599
Replies
6
Views
181
  • Last Post
Replies
6
Views
557
Replies
6
Views
755
Replies
1
Views
1K
Replies
2
Views
918
  • Last Post
Replies
9
Views
637
Top