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590 Chapter Eleven DIFFERENTIAL EQUATIONS 25. Pick out wh tial equatior (if any) is V Cr" a 21, (a) For what values of C, and than one eq than one so solution to the differential equation = 2, what dy (b) dy (c) dr (b) If the solution satisfies U = 40 when more (if anything) can you say about C and n? Find the value of Aso that the equation U,-ry-รฃยยง 0 has a solution of the form y(z) = A + Be?/2 for any constant B 22. (a) (b) If y(0) = 1, find B. 23. In Figure 11.3, the height, y, of the hanging cable above d2 e horizontal line satisfies 26. Families e +e satisfies this differential equations ential equ (a) Show that y equation if k = 1. (b) For general k, one solution to this differential equa- tion is of the form 2A Substitute this expression for y into the differential equation to find A in terms of k. Cable 27. Is g() Figure 11.3 28. (a) Let 24. Match solutions and differential equations. (Note: Each an equation may have more than one solution.) (I) y=e" xy,-6y = 0 Gi (b) If (c) (III) y=e-z Gi Strengthen Your Understanding blems 29-30, explain what is wrong with the statement. 33. A diffe 29, Q = 6e4t is the general solution to the differential equa- differe 34. A diff tion dQ /dt = 4Q.