Explanation Given: The given equation is d P d t = ( k cos t ) P . Calculation: Consider the equation. d P d t = ( k cos t ) P ...... ( 1 ) Now, d P d t = ( k cos t ) P d P P = ( k cos t ) d t Integrate both sides. ∫ d P P = k ∫ ( cos t ) d t ln ( P ) = k sin t + c 1 P = e k sin t + c 1 P = e c 1 × e k sin t That is, P = c e k sin t

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Differential Equations

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Chapter 3.1, Problem 42E

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To find: The solution of the differential equation dPdt=(kcost)P for initial condition P(0)=P∘ and show the graph of the solution.

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Chapter 3.1, Problem 41E

Chapter 3.1, Problem 43E

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FIRST COURSE IN DIFF.EQ.-WEBASSIGN

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The solution of the differential equation d P d t = ( k cos t ) P for initial condition P ( 0 ) = P ∘ and show the graph of the solution.

Solution Summary: The author explains how to find the solution of the differential equation dPt=(kmathrmcos

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To find: The solution of the differential equation dPdt=(kcost)P for initial condition P(0)=P∘ and show the graph of the solution.

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Chapter 3 Solutions