Problem_1.7soln

# Warns us that some solutions may not be found this is

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warns us that some solutions may not be found. This is not of concern for us as the solution that is found is the one we need (other solutions may lie in the complex plane ) sol2 = First @ Flatten @ Solve @H P @ t D ê .sol ê .t Ø 0 L ã P0, C @ 1 DDDD — Solve::ifun : Inverse functions are being used by Solve, so some solutions may not be found; use Reduce for complete solution information. More… C @ 1 D Ø Log @ 1 - P ÅÅÅÅÅ P0 D ÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅ ÅÅÅÅÅÅÅÅÅÅÅÅÅ P Then we substitute for the value of C[1] into our general solution to get P @ t D ê .sol ê .sol2 kt P ÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅ ÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅ - 1 + ‰ kt + P ÅÅÅÅÅ P0 To determine partial fractions we can use the Apart function Apart A 1 ÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅ ÅÅÅÅÅÅÅÅÅ P - P 2 ê P E 1 ÅÅÅÅ P + 1 ÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅ - P + P 2 Problem_1.7.nb
• Summer '13
• LeThuy
• Elementary algebra, DSOLVE, P¶, Ø ÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅ

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