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Calculus Level 4

Find J ( 0 ) J''(0) if x J ( x ) + J ( x ) + x J ( x ) = 0 xJ''(x)+J'(x)+xJ(x)=0 for all x J ( 0 ) = 1 J(0)=1 and J ( 0 ) J\prime \prime \prime (0) exists

J ( x ) J'''(x) , J ( x ) J''(x) , J ( x ) J'(x) are the third, second and first derivative of the function J ( x ) J(x)

(Bilkent University, 1st Midterm Question)


The answer is -0.5.

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1 solution

Abhishek Sinha
Oct 27, 2014

Differentiate the given expression once w.r.t. x x and then put x = 0 x=0 .

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