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welcome to AI electron line so far weamp;#39;ve used a characteristic equation to solve homogeneous differential equations that had two distinct real roots what happens when the equation has real but repeated roots with other words the two roots are exactly the same hereamp;#39;s an example of that letamp;#39;s again find the characteristic equation and solve it and see what we get so this becomes R squared plus two times R plus one equals zero this is the characteristic equation that looks just like a quadratic equation but we use R instead of X now when we solve this we can factor this we can say that this is equal to R plus 1 times R plus 1 equals 0 and that means that we have two roots r1 equals negative 1 and r2 equals negative 1 in other words the root is repeated we get the same real value then if we want to turn that into the general solution to this differential equation itamp;#39;ll look as follows this will look close follow so we have Y letamp;#39;s say itamp;#39;s a
