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1. Fundamental theorem. Prove it for second-order PDEs in two and three independent variables. Hint. Prove it by substitution. 2-13 VERIFICATION OF SOLUTIONS Verifiy (by substitution) that the given function is a solution of the PDE. Sketch or graph the solution as a surface in space. 2-5 Wave Equation (1) with suitable c 2 2. u = x² + 1² 3. u cos 4t sin 2x 4. u = sin kct cos kx 5. usin at sin bx

1. Fundamental theorem. Prove it for second-order PDEs in two and three independent variables. Hint. Prove it by substitution. 2-13 VERIFICATION OF SOLUTIONS Verifiy (by substitution) that the given function is a solution of the PDE. Sketch or graph the solution as a surface in space. 2-5 Wave Equation (1) with suitable c 2 2. u = x² + 1² 3. u cos 4t sin 2x 4. u = sin kct cos kx 5. usin at sin bx

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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1. Fundamental theorem. Prove it for second-order PDEs in two and three independent variables. Hint. Prove it by substitution. 2-13 VERIFICATION OF SOLUTIONS Verifiy (by substitution) that the given function is a solution of the PDE. Sketch or graph the solution as a surface in space. 2-5 Wave Equation (1) with suitable c 2 2. u = x² + 1² 3. u cos 4t sin 2x 4. u = sin kct cos kx 5. usin at sin bx
Transcribed Image Text:1. Fundamental theorem. Prove it for second-order PDEs in two and three independent variables. Hint. Prove it by substitution. 2-13 VERIFICATION OF SOLUTIONS Verifiy (by substitution) that the given function is a solution of the PDE. Sketch or graph the solution as a surface in space. 2-5 Wave Equation (1) with suitable c 2 2. u = x² + 1² 3. u cos 4t sin 2x 4. u = sin kct cos kx 5. usin at sin bx
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