Find the solution of the differential equation dP/dt = sqrt (P*t) that satisfies the initial condition P (1) = 5. Answer: P (t) = ...

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Mathematics

Damon

18 October, 01:02

Find the solution of the differential equation dP/dt = sqrt (P*t) that satisfies the initial condition P (1) = 5. Answer: P (t) = ...

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Layne Rosales · Answer 1

Sqrt of (1/P) = √t dt

integrate both sides and use initial conditions 2 (5) ^1/2 = 2/3 (1) ^3/2 + C

C = 2√5 - 2/3

therfore

P (t) = (2/6 t ^ 2/3 + √5 - 2/6) ^ 2