Test 2 Review 1

Test 2 Review 1 - Math 122 Test 2 - Review 1 1 Differential...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

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

Unformatted text preview: Math 122 Test 2 - Review 1 1 Differential Equations 1.1 Slope Fields Sketch the slope field and a likely solution curve for: 1. dy dx = y- x- 1 y (0) = 1 2. dy dx = x 2 + y 2 y (0) = 1 3. dy dx = 2 x- 3 y y (0) = 1 1.2 Euler’s Method Use Euler’s method with h = 0 . 1 to approximate y (1) for the initial value problem: 4. dy dx = y- x- 1 y (0) = 1 5. dy dx = x 2 + y 2 y (0) = 1 6. dy dx = 2 x- 3 y y (0) = 1 1.3 Separable Solve the following differential equations: 7. y = 3( y + 7) x 2 8. y = x 3 y 2 9. y = 4- 2 x 3 y 2- 5 ; y (1) = 3 10. y = 2 y- 3; y (0) = 2 11. y = y + 1; y (0) = 1 12. y = 3 x 2 y 2 ; y (0) = 1 1.4 Linear Solve the following differential equations: 13. y + (cot x ) y = 5 e cos x 14. x 3 y + (2- 3 x 2 ) y = x 3 15. y + 3 x y = sin x x 3 16. xy + 2 y = 4 x 2 17. x (ln x ) y + y = 2 ln x 18. y + (cot x ) y = 3 sin x cos x 19. y + 2 y = 2 x 20. y + 1 x y = sin x 21. xy = x- y y (2) = 1 22. y- 2 y x +1 = ( x 2 + 2 x + 1) 2 y (0) = 1 1.5 Applications 23. A tank contains 20 kg of salt dissolved in 5000 L of water. Brine that contains 0.03 kg of salt per liter of water enters the tank at a rate of 25 L/min. The solution is kept thorughly mixed and drains from the tank at the same rate. How much salt remains in the tank after half an hour?...
View Full Document

This note was uploaded on 02/17/2010 for the course MATH 122 taught by Professor Butler during the Spring '07 term at Case Western.

Page1 / 4

Test 2 Review 1 - Math 122 Test 2 - Review 1 1 Differential...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online