In Exercises 5360, write a system of inequalities to describe the region.

Math246 Week 7: Solving Differential Equations with Real Roots We will continue where we left off last time with solving differential equations with two real roots. This is not every difficult as it just requires you know how to factor and how to memorize. Examples '' ' ' 1. y +10y +30y=0 y(0 =6 y (0)=10 The quadratic we need to satisfy is 2 w +10w+30=0 We can factor this as w+3 )w+10 )=0 So our roots are −3 and −10 −3t −10t So our general solution is y(t)=ae +be y'(t=−3ae −3−10be −10t And its derivative is Now we have t