Chapter Notes (2)

See example 22 dx 1 by computing 2 verify that for any

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

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: y = xe x + Ce x is a solution of dx dy the differential equation = e x + y . (See Example 2.2.) dx 1. By computing 2. Verify that for any constant C the expression y = x 2 − 2 x + C is a solution of the differential dy x − 1 = . equation dx y 3. a) Verify that for any constant C the expression y = x − 1 + Ce − x is a solution of the dy differential equation = x− y. dx b) Find the solution of the differential equation in 3a) that satisfies y (0) = 2 . 4. a) Verify that for any constant C the expression y = equation dy 1 + xy = . dx 1 + x Ce x − 1 is a solution of the differential 1+ x b) Find the solution of the differential equation in 4a)that satisfies y (1) = 2 . 5. a) Verify that for any constant C ≥ 0 the expression y = − x + 2 x 2 + C is a solution of the dy x − y differential equation = . dx x + y b) Find the solution of the differential equation in 5a) that satisfies y (1) = 1 . 6. Which, if any, of the differential equations in exercises 1 - 5 are separable? 7. Which, if any, of the following differential equations are separable? 27 2 Differential Equations a) dy xy = dx 1 + x b) dy xy = dx y + x c) dy = (3 y + 1) 2 dx d) dy 1 + y 2 = dx 1 + x 2 Use separation of variables to solve each of the differential equations in exercises 8 - 16 below: 8. dy = xy , y (0) = 2 . dx 9. dy = 2 y 2 x , y (0) = 2 dx 10. dy = dt 11. dy t = 2 y , y (0) = 1 . dt e 12. dy = 3 y + 1 , y (1) = 2 . dt 13. y′ = y ( x + 1) , y (0) = 2 . 14. dy 2y = , y (0) = 3 . dx x + 1 15. y′ = 16. dy 1 + 2 y = dx 1 + x t , y (1) = 3 y +1 2(t + 1) , y (0) = 2 . y 17. After 5 years, which of the following accounts will have a larger principal? After 10 years? Justify your answers. a) An account earning 5% annual interest compounded continuously and starting out with $1000. b) An account earning 4% annual interest compounded continuously and starting out with $1100. 18. a) Suppose you want to put away a certain amount of money so that in 10 years the principal will be $10,000. If you can invest at 6% annual interest compounded conti...
View Full Document

This document was uploaded on 04/06/2014.

Ask a homework question - tutors are online