{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

126_pdfsam_math 54 differential equation solutions odd

# 126_pdfsam_math 54 differential equation solutions odd - H...

This preview shows page 1. Sign up to view the full content.

Chapter 3 Solving this separable equation yields T ( t ) = 19 . 17 + Ce 3 t . When t = 0 we are given T (0) = 55. Using this information to solve for C gives C = 35 . 83. Hence, the van temperature is given by T ( t ) = 19 . 17 + 35 . 83 e 3 t . To find out when the temperature in the van will reach 27 C, we let T ( t ) = 27 and solve for t . Thus, we see that 27 = 19 . 17 + 35 . 83 e 3 t e 3 t = 7 . 83 35 . 83 0 . 2185 t ln(0 . 2185) 3 0 . 5070 (hr) or 30 . 4 min . 13. Since the time constant is 64, we have K = 1 / 64. The temperature in the tank increases at the rate of 2 F for every 1000 Btu. Furthermore, every hour of sunlight provides an input of 2000 Btu to the tank. Thus,
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: H ( t ) = 2 × 2 = 4 ◦ ± per hr . We are given that T (0) = 110, and that the temperature M ( t ) outside the tank is a constant 80 ◦ ±. Hence the temperature in the tank is governed by dT dt = 1 64 [80 − T ( t )] + 4 = − 1 64 T ( t ) + 5 . 25 , T (0) = 110 . Solving this separable equation gives T ( t ) = 336 + Ce − t/ 64 . To Fnd C , we use the initial condition to see that T (0) = 110 = 336 + C ⇒ C = − 226 . This yields the equation T ( t ) = 336 − 226 e − t/ 64 . 122...
View Full Document

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern