If z = x2 – y2 and x = t cos 2r and y = r sin t , then a²z is (A) 2 cos?(2r) + 2r² cos²(t) – 2ry sin t (B) –8tx cos 2r + 8t2 sin 2r + 2 sin? t (C) 2 cos?(2r) – 2r? cos?(t) + 2ry sin t (D) –8tx cos 2r + 8t?sin?(2r) – 2 sin? t (E) -4x sin 2r – 2t sin 4r + 2y cos t + r sin 2t

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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If z = x? – y² and x = t cos 2r and y = r sint , then
a2z
is
(A) 2 cos?(2r) + 2r² cos?(t) – 2ry sin t
(B) -8tx cos 2r + 8t2 sin 2r + 2 sin? t
(C) 2 cos? (2r) – 2r? cos? (t) + 2ry sin t
(D) -8tx cos 2r + 8t?sin? (2r) – 2 sin? t
(E) -4x sin 2r – 2t sin 4r + 2y cos t +rsin 2t
Transcribed Image Text:If z = x? – y² and x = t cos 2r and y = r sint , then a2z is (A) 2 cos?(2r) + 2r² cos?(t) – 2ry sin t (B) -8tx cos 2r + 8t2 sin 2r + 2 sin? t (C) 2 cos? (2r) – 2r? cos? (t) + 2ry sin t (D) -8tx cos 2r + 8t?sin? (2r) – 2 sin? t (E) -4x sin 2r – 2t sin 4r + 2y cos t +rsin 2t
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