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In Problems 1 through 16, transform the given differential equation or system into an equivalent system of first-order dif- ferential equations. 1. x" + 3x' + 7x =12 2. x" + 4x -x3 = 0 (This equation is used in Section 6.4 to describe the motion of a mass connected to a "soft" spring.) w.konkur.in 236 Chapter 4 Introduction to Systems of Differe 8. 13 x(3) - 212x" + 3tx' + 5x = Int 9. x (3) = (x')2 + cosx 10. x" - 5x + 4y = 0, y" + 4x - 5y =0 kx 11. x" = - ky ( x 2 + 12 ) 3/ 2 ' ' (x2+ 12) 3/2 (These equa- tions are used in Application 4.3 to describe the motion of a satellite in elliptical orbit around a planet.) 12. 3x" = 2y', 3y" =-2x' 13. x" = -75x +25y, y" = 50x - 50y + 50cos 5t (This sys- tem of equations is used in Section 5.4 to describe the mo- tions of a double mass-and-spring system.) 31 14. x" + 3x' + 4x - 2y = 0, y" + 2y' - 3x + y= cost 15. x" = 3x - y + 2z, y" = x + y - 4z, z" = 5x - y -z 16. x" = (1 - y)x, y" = (1 -x)y