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# wksht01sol - MATH 152 L1& L2 Applied Linear Algebra and...

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Unformatted text preview: MATH 152 L1 & L2 Applied Linear Algebra and Differential Equations Spring 2004-05 ¥ Week 01 Worksheet Solutions : First-order differential equations Q1. (Linear vs. nonlinear) Indicate whether the following equation is linear or nonlinear . 1. dy dt + 3 t 2 y = 0 linear . 7. dy dt = t + sin y . 2. y + y 2 = t . 8. dy dt ¶ 2 = y . 3. dy dt = 2 ty 2 t 2- y 2 . 9. y + y = sin- 1 t 2 , | t | < 1 . 4. dy dt + 2 y = e 2 t . 10. dy dt = 2 t- y y- t . 5. y = t p 1 + y 2 . 11. dy dt = te y + t . 6. y dy dt + ty = t . 12. dx dt + 2 t + 1 2 t x = 2 x + 1 2 t . Solution 1. linear 2. nonlinear 3. nonlinear 4. linear 5. nonlinear 6. nonlinear 7. nonlinear 8. nonlinear 9. linear 10. nonlinear 11. nonlinear 12. linear Q2. (i) (Direction field) Match the graph of the direction field to the differential equation and give a brief justification for your choice. –3 –2 –1 1 2 3 y(t) –3 –2 –1 1 2 3 t (a) dy dt =- ty ....
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## This note was uploaded on 09/30/2010 for the course MATH MATH152 taught by Professor Kcc during the Spring '10 term at HKUST.

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wksht01sol - MATH 152 L1& L2 Applied Linear Algebra and...

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