Please answer this question::(e^x +1)ydy - (y2+1)e^xdx = 0Given x=0 y=0
Aniket debnath , 5 Years ago
Grade 11
Integral Calculus> Please answer this question:: (e^x +1)ydy...
4 Answers
Arun
Last Activity: 5 Years ago
Dear student
It can be written as
y dy/(y^2 +1) = e^x dx /(e^x + 1)
Now I think you can do.
If you find any difficulty, please feel free to ask me again.
Aniket debnath
Last Activity: 5 Years ago
Please sir do the full solution
I have done 70% of the problem but can't go further please help.......
Samyak Jain
Last Activity: 5 Years ago
(ex + 1)ydy – (y2 + 1)exdx = 0
2ydy/(y2 + 1) = 2ex dx /(ex + 1)
Now if y2 + 1 = t, then differentiating both sides we get 2ydy = dt
and similarly ex + 1 = u, then ex dx = du
ln(t) = 2 ln(u) + lnc , where I’ve taken lnc as constant of integration and ln(t) means loge(t).
ln(t) – 2 ln(u) = lnc i.e. ln(t) – ln(u)2 = lnc or ln(t/u2) = lnc
Substitute t as y2 + 1 and u as ex + 1 to get
(y2 + 1)/(ex + 1)2 = c [You can rearrange the result to get the desired answer.]
Samyak Jain
Last Activity: 5 Years ago
Apply the condition : x = 0, y = 0 to get constant c
(y2 + 1)/(ex + 1)2 = c
(02 + 1) / (e0 + 1)2 = c = 1/(2)2 = 1/4
(y2 + 1) / (ex + 1)2 = 1/4
i.e. 4(y2 + 1) = (ex + 1)2
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