Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Answer 2 Only
1. Use separation of variables to find a product solution to the following: a²u k -U= dx2 A. B. C. D. B. C. Hint: No need to separate into 3 cases A. D. u = e-t (A₁eka²t cosh ax + B₁eka²t sinh ax) u = e-t (A₂e-ka²t cos ax + B₂e-ka²t sin ax) u = e-t (A3x + B3) -ka²t u=e¹ (A₁e-ka²t cosh ax + B₁e sinhax) u = et (A₂eka²t cos ax + B₂eka²t sin ax) u = et (A3x + B3) 2. Use separation of variables to find a product solution to the following: ди at u = e-t e-t(A₁e-ka²t cosh ax + B₁e-ka²t sinh ax) u = e-t (A₂eka²t cos ax + B₂eka²t sin ax) u = e-t (A3x + B3) u = et (A₁eka²t cosh ax + B₁eka²t sinh ax) u = et (A₂e-ka²t cos ax + B₂e-ka²t sin ax) u = et (A3x + B3) X du əx = y u = C₁ k> 0 du dy u = C₁ C₂ G₂₁ (1) ²² u = C₁x²²yC₂-1 u = c₁(xy) c2
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Transcribed Image Text:1. Use separation of variables to find a product solution to the following: a²u k -U= dx2 A. B. C. D. B. C. Hint: No need to separate into 3 cases A. D. u = e-t (A₁eka²t cosh ax + B₁eka²t sinh ax) u = e-t (A₂e-ka²t cos ax + B₂e-ka²t sin ax) u = e-t (A3x + B3) -ka²t u=e¹ (A₁e-ka²t cosh ax + B₁e sinhax) u = et (A₂eka²t cos ax + B₂eka²t sin ax) u = et (A3x + B3) 2. Use separation of variables to find a product solution to the following: ди at u = e-t e-t(A₁e-ka²t cosh ax + B₁e-ka²t sinh ax) u = e-t (A₂eka²t cos ax + B₂eka²t sin ax) u = e-t (A3x + B3) u = et (A₁eka²t cosh ax + B₁eka²t sinh ax) u = et (A₂e-ka²t cos ax + B₂e-ka²t sin ax) u = et (A3x + B3) X du əx = y u = C₁ k> 0 du dy u = C₁ C₂ G₂₁ (1) ²² u = C₁x²²yC₂-1 u = c₁(xy) c2
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