
Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class
Forming Differential equations
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Forming Differential equations
Last updated at May 29, 2023 by Teachoo
Question 11 Which of the following differential equations has π¦=π1π^π₯+π2π^(βπ₯) as the general solution ? (A) (π^2 π¦)/(ππ₯^2 )+π¦=0 (B) (π^2 π¦)/(ππ₯^2 )βπ¦=0 (C) (π^2 π¦)/(ππ₯^2 )+1=0 (D) (π^2 π¦)/(ππ₯^2 )βπ¦=0 π¦=π1π^π₯+π2π^(βπ₯) β΄ Differentiating both sides w.r.t. π₯ ππ¦/ππ₯ =π1π^π₯βπ2π^(βπ₯) Again Differentiating both sides w.r.t. x (π^2 π¦)/(ππ₯^2 ) =π1π^π₯βπ2π^(βπ₯) (β1) Since it has two variables, we will differentiate twice (π^2 π¦)/(ππ₯^2 ) =π1π^π₯+π2π^(βπ₯) (π^2 π¦)/(ππ₯^2 )=π¦ (π^2 π¦)/(ππ₯^2 ) βπ¦=0 β΄ Option B is correct (Putting π¦=π1π^π₯+π2π^(βπ₯))