William Curry
2021-12-29
Answered

Find the general solution of the given differential equations

$4y\prime \prime -4y\prime -3y=0$

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Find Laplace transform for

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Find the laplace transform of

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Half-life of a DNA of an extinct moa is 521 years. A 1 mg sample was estimated to be 6000 years old. Determine the initial amount of the DNA sample.

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Applications of First Order Differential Equations: A dead body was found within a closed room of a house where the temperature was a constant ${24}^{\circ}C$ . At the time of discovery, the core temperature of the body was determined to be ${28}^{\circ}C$ . One hour later, a second measurement showed that the core temperature of the body was ${26}^{\circ}C$ . The core temperature of the body at the time of death is ${37}^{\circ}C$ . A. Determine how many hours elapsed before the body was found. B. What is the temperature of the body 5 hours from the death of the victim?

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Need to evaluate the Laplace integral transform (definition below) of $\sqrt{t}$ using complex analysis. How is that possible?

$$\hat{f}(s)={\int}_{0}^{\mathrm{\infty}}\sqrt{t}{e}^{-st}dt$$

$$\hat{f}(s)={\int}_{0}^{\mathrm{\infty}}\sqrt{t}{e}^{-st}dt$$

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Without using the shift formula prove that Laplace of

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asked 2021-11-14

Find the general solution of the given differential equation.

${y}^{\left(6\right)}+y=0$