text: # Differential equation, confused on directions, F(x,y)?
  
  1. Jan 18, 2006
  
  ### mr_coffee
  
  Hello everyone, I am confused on what they are wanting me to do here on this problem:
  
  has an implicit general solution of the form
  
  In fact, because the differential equation is separable, we can define the solution curve implicitly by a function in the form
  
  Find such a solution and then give the related functions requested.
  
  here is my work, i think they wanted me to do, they gave no intial condition so i solved for C:
  
  but it was incorrect
  
  2. Jan 18, 2006
  
  ### Benny
  
  Well what is supposed to be the correct answer? I can't see much wrong with what you've done.
  
  Edit: You seem to have replaced the y with x after the integration of the exponential.
  
  Last edited: Jan 18, 2006
  3. Jan 18, 2006
  
  ### mr_coffee
  
  thats a good question, it doesn't tell me. it will tell me if i get it right, not if i get it wrong. Whats this implicit general solution stuff do i have to take partial derivatives or somthing?
  
  4. Jan 18, 2006
  
  ### HallsofIvy
  
  Staff Emeritus
  WHY do you keep writing $\frac{1}{e^{-2x}}$? Surely you know that $\frac{1}{e^{-2x}}= e^{2x}$
  
  Your instructions were to write the answer as F(x,y)= K and then write it as F(x,y)= G(x,y)+ H(x,y)= K
  
  You already have 5e2x- arcsin(x/2)= K. Can't you just look at that and pick G and H?
  
  5. Jan 18, 2006
  
  ### benorin
  
  Going from the second line to the third line your "y" became an "x". As far as what they want:
  
  They asked for $$F(x,y)=G(x)+H(y)=K$$
  
  So "Find such a solution" is satisfied by $$F(x,y)=-\mbox{arcsin}\left( \frac{x}{2}\right) + 5e^{2y} = K$$
  
  but the answer they want is "give the related functions requested"
  
  so try $$G(x)= -\mbox{arcsin}\left( \frac{x}{2}\right) \mbox{ and }H(y)= 5e^{2y}$$
  
  6. Jan 18, 2006
  
  ### mr_coffee
  
  Ahhh, thanks so much everyone it was correct. weee
metadata: {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}