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Math 4B Practice Midterm 1 Name: Determine the order of the following equations involving y ( x ). ( 1 pt ea. ) 1. y (4) + xy (5) = x 6 2. y 00 - log( x ) = 5 y 000 3. y 0 e y + ye y 0 = 0 4. sin( y 0 ) = y 00 5. x 2 log( y ) - y 0 = cos( y ) Solve each equation for u ( t ). ( 3 pt ea. ) 6. u 0 = e - u , u ( e ) = 1 , t > 0 7. uu 0 + t 2 u 2 = 0 , u ( - 3) = e 9 , u > 0 8. u = u 0 + t, u (0) = - 1 9. u 0 = u 2 u - t , u (1) = 1 , t > 0 10. u 0 + t - 1 u + t - 2 = 0 , u (1) = 0 , t > 0
Find the equilibrium solutions of y ( t ) and indicate if each is stable, unstable, or semistable. ( 5 pts ea. ) 11. y 0 = y 2 - y 12. y 0 = y 3 - y 2 Extra Credit Question

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