{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

chapter2.page10

# chapter2.page10 - = 2 y x 3 cos x(d y = 2 xy 3 x 2 e x 2(e...

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

10 1. EXPLICITLY SOLVABLE FIRST ORDER DIFFERENTIAL EQUATIONS a Example 3.2 . If in Example 3.1, we set k = 0 . 2 and ω = π 4 , we would have general solution T ( t ) = e - 0 . 2 t ˆ 80 e 0 . 2 t - 5 3 . 2 0 . 64 + π 2 e 0 . 2 t cos( ωt )+ 4 π 0 . 64 + π 2 e 0 . 2 t sin( ωt ) + C ! The following graph displayed curves of several solutions with different initial values T (0) . Figure 6. Greek Letter Bar The picture above exhibits the situation when the air condition fails at t = 0, so after a out 14 hours, the room temperature is the same as the outside temperature! Practice (1) Find general solution to the following problem (a) y 0 + 4 xy = x 2 (b) e x y 0 + e x y = sin( x ) (c) xy
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: = 2 y + x 3 cos( x ) (d) y = 2 xy + 3 x 2 e x 2 (e) ( x 2 + 4) y + 3 xy = x (f) ( x 2 + 1) y + 3 x 3 y = 6 xe-3 2 x 2 (2) Application: The equation y = ky models wide range of natural phenomena–any involving a quantity whose time rate of change is proportional to its current size. Continuously Compounded Interest Rate: Let P ( t ) denote principle at time t, which will earn interest with rate r ( t ) and compounded continuously, we have dP dt = rP. Now...
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