Differential Equations: Finding the General Solutionby amsscorpio Tags: differential, equations, solution 

#1
Sep209, 07:31 PM

P: 3

Hello, this is the first time I post here, I'm really stumped and tried everything, even my TI89 calculator won't give me something nice XD
1. The problem statement, all variables and given/known data Find the general solution of dy/dt= 1/(ty+t+y+1) 2. Relevant equations No relevant equations. 3. The attempt at a solution The first step I did was, (ty+t+y+1)dy = 1dt by cross multiplying proportions. I can't figure out anyway to seperate my terms to the proper places...I then tried this: integral( ty+t+y+1 dy ) = integral( 1dt ) and resulted in: ty^2/2 + ty + y^/2 + y + c = t But this leads me nowhere...Any ideas? Or should I come into conclusion that this differential equation is not valid and unable to do? 



#2
Sep209, 07:48 PM

P: 3

Ahh I THOUGHT I tried everything XD simple algebra error...
I found that (ty + t + y + 1) = (t + 1)(y + 1). when factored... then my next step would be (y + 1) dy = dt/(t + 1). which then i can integrate both sides to give me y^2/2 + y + c = lnt+1 + c solving for y ultimately gives me y = + or  (sqrt( 4lnt+1 +1 ) +1 )/2 All over 2. Am I right? 



#3
Sep209, 08:00 PM

HW Helper
P: 6,213

But just know that when you have things like y^{2}+y^{3}=ln(x^{2}+x+1)+e^{87x}+x^{3}+C you don't always need to make 'y' the subject of the formula, you can leave it as is. 



#4
Sep209, 08:02 PM

Mentor
P: 20,997

Differential Equations: Finding the General Solution 



#5
Sep209, 08:03 PM

P: 3

Ahh I don't know how to choose best answer + feedback on yahoo answers lol, I did it to have more chances of geting help, thank you and yes I will remember that.



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