Test 2 Review 1

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

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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?...
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## 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.

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

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