Solution Found!
Explain why or why not Determine whether the
Chapter 7, Problem 41E(choose chapter or problem)
Explain why or why not Determine whether the following statements are true and give an explanation or counter-example.
a. The general solution of \(y^{\prime}(t)=20 y\) is \(y=e^{20 t}\).
b. The functions \(y=2 e^{-2 t}\) and \(y=10 e^{-2 t}\) do not both satisfy the differential equation \(y^{\prime}+2 y=0\).
c. The equation \(y^{\prime}(t)=t y+2 y+2 t+4\) is not separable.
d. A solution of is \(y^{\prime}(t)=2 \sqrt{y}\) is \(y=(t+1)^{2}\).
Questions & Answers
QUESTION:
Explain why or why not Determine whether the following statements are true and give an explanation or counter-example.
a. The general solution of \(y^{\prime}(t)=20 y\) is \(y=e^{20 t}\).
b. The functions \(y=2 e^{-2 t}\) and \(y=10 e^{-2 t}\) do not both satisfy the differential equation \(y^{\prime}+2 y=0\).
c. The equation \(y^{\prime}(t)=t y+2 y+2 t+4\) is not separable.
d. A solution of is \(y^{\prime}(t)=2 \sqrt{y}\) is \(y=(t+1)^{2}\).
ANSWER:Problem 71EThe average time until a computer chip fails (see Exercise 70) is . Find this value.Electronic chips Suppose the probability that a particular computer chip fails after t = a hours of operation is .a. Find the probability that the computer chip fails after 15,000 hr of operation.b. Of the chips that are still operating after 15,000 hr. what fraction of these will operate for at least another 15,000 hrc. Evaluate and interpret its meaning.Solution:Step 1To find the probability that the computer chip fails after 15,000 hr of operation.We need to evaluate the integral , Hence the probability that the computer chip fails after 15,000 hr of operation is 0.472.