If (a+bx)e^(y/x)=x then prove that x (d^2 y)/(dx^2 )=(a/(a+bx))^2
The rest of the post is locked. Join Teachoo Black to see the full post.
CBSE Class 12 Sample Paper for 2024 Boards
Question 2
Question 3 Important
Question 4 Important
Question 5 Important
Question 6 Important
Question 7
Question 8
Question 9
Question 10
Question 11
Question 12
Question 13 Important
Question 14 Important
Question 15 Important
Question 16
Question 17 Important
Question 18
Question 19 [Assertion Reasoning] Important
Question 20 [Assertion Reasoning]
Question 21 (Choice 1) Important
Question 21 (Choice 2)
Question 22 Important
Question 23 (Choice 1)
Question 23 (Choice 2) Important
Question 24
Question 25
Question 26 Important
Question 27
Question 28 (Choice 1)
Question 28 (Choice 2) Important
Question 29 (Choice 1)
Question 29 (Choice 2)
Question 30 (Choice 1) Important
Question 30 (Choice 2)
Question 31 You are here
Question 32 Important
Question 33 (Choice 1)
Question 33 (Choice 2) Important
Question 34 Important
Question 35 (Choice 1) Important
Question 35 (Choice 2) Important
Question 36 (i) [Case Based]
Question 36 (ii)
Question 36 (iii) (Choice 1)
Question 36 (iii) (Choice 2)
Question 37 (i) [Case Based]
Question 37 (ii)
Question 37 (iii) (Choice 1) Important
Question 37 (iii) (Choice 2)
Question 38 (i) [Case Based]
Question 38 (ii)
CBSE Class 12 Sample Paper for 2024 Boards
Last updated at April 8, 2024 by Teachoo
The rest of the post is locked. Join Teachoo Black to see the full post.
Given (𝑎+𝑏𝑥)𝑒^(𝑦/𝑥)=𝑥 𝒆^(𝒚/𝒙) = 𝒙/((𝒂 + 𝒃𝒙)) Taking log on both sides log 𝑒^(𝑦/𝑥) = log 𝑥/((𝑎 + 𝑏𝑥)) 𝒚/𝒙 𝐥𝐨𝐠 𝐞 = log x – log (a + bx) 𝑦/𝑥 × 1= log x – log (a + bx) 𝒚/𝒙 = log x – log (a + bx) Differentiating w.r.t x 𝑑(𝑦/𝑥)/𝑑𝑥 = 1/𝑥 – 1/(𝑎 + 𝑏𝑥) × 𝑏 (𝒅𝒚/𝒅𝒙 𝐱 − 𝒚)/𝒙^𝟐 = 1/𝑥 – 𝑏/(𝑎 + 𝑏𝑥) (𝑦^′ x−y)/𝑥^2 = (𝑎 + 𝑏𝑥 − 𝑏𝑥)/(𝑥(𝑎 + 𝑏𝑥)) 𝑦^′ x−y = 〖𝑎𝑥〗^2/(𝑥(𝑎+𝑏𝑥)) 𝒚^′ 𝐱−𝐲 = 𝒂𝒙/(𝒂+𝒃𝒙) Differentiating again w.r.t x (𝐝(𝒚^′ )/𝒅𝒙 𝒙+𝒚^′ 𝒅𝒙/𝒅𝒙) − 𝒅𝒚/𝒅𝒙 = (𝒂( 𝒂 + 𝒃𝒙) − 𝒃(𝒂𝒙))/〖(𝒂 + 𝒃𝒙)〗^𝟐 𝑦^′′ 𝑥+𝑦^′−𝑦^′= (𝑎^2 + 𝑏𝑎𝑥 − 𝑏𝑎𝑥)/〖(𝑎 + 𝑏𝑥)〗^2 𝑦^′′ 𝑥 = 𝑎^2/〖(𝑎 + 𝑏𝑥)〗^2 𝒙 (𝒅^𝟐 𝒚)/(𝒅𝒙^𝟐 )=(𝒂/(𝒂 + 𝒃𝒙))^𝟐 Hence proved