1. Consider the curve F(x, y) = 0. Show that if F has continuous second derivatives, then a formula for the second derivative of y is FF22FFF + FF2 d²y dx² F3 Y

Advanced Engineering Mathematics
10th Edition
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Chapter2: Second-order Linear Odes
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1. Consider the curve F(x, y) = 0. Show that if F has continuous second derivatives, then
a formula for the second derivative of y is
Fax F2 - 2Fay FxFy + FyyF2
xy
d²y
dx²
y
(Hint: This question really tests your understanding of the chain rule!)
Transcribed Image Text:1. Consider the curve F(x, y) = 0. Show that if F has continuous second derivatives, then a formula for the second derivative of y is Fax F2 - 2Fay FxFy + FyyF2 xy d²y dx² y (Hint: This question really tests your understanding of the chain rule!)
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