Verify that `y=log(x+sqrt(x^2+a^2))` satisfies the differential equati – InterviewSolution

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1.	Verify that `y=log(x+sqrt(x^2+a^2))` satisfies the differential equation `d^2y/(dx^2)+x(dy)/(dx)=0`
Answer» `y=log"("x+sqrt(x^(2)+a^(2))")"` `implies(dy)/(dx)=(1)/((x+sqrt(x^(2)+a^(2)))).{1+(2x)/(2sqrt(x^(2)+a^(2)))}impliesy_(1)=(1)/(sqrt(x^(2)+a^(2)))` `impliesy_(1)^(2)(x^(2)-a^(2))=1impliesy_(1)^(2)(2x)+(x^(2)+a^(2))2y_(1)y_(2)=0` `(x^(2)+a^(2))y_(2)+xy_(1)=0.`

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