if y=log [x+root (x^2+a^2) then show that (x^2+a^2)d2y/dx2+xdy/dx=0 - Maths - Continuity and Differentiability

Question

if y=log [x+root (x^2+a^2) then show that (x^2+a^2)d2y/dx2+xdy/dx=0

Neha Sethi · Accepted Answer

Dear student
We have, y=logx+x2+a2Differentiating wrt x⇒dydx=1x+x2+a2×ddxx+x2+a2=1x+x2+a21+2x2x2+a2⇒dydx=1x+x2+a2×x+x2+a2x2+a2⇒y1=1x2+a2, where y1=dydx⇒y12x2+a2=1Differentiating wrt x we get⇒y12ddxx2+a2+x2+a2
ddxy12=0y12
2x+x2+a2+2y1y2=02y1y2x2+a2+xy1​​=0  y1≠0
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