Recall from our lesson that a Non - Homogenous 2nd Order Differential Equation has 2 sides: The Characteristic Side and the Particular Side. y" - 3y' - 10y = 5 e-2 The Left Side has our dependent variables (usually the letter y) and is our Characteristic Side, while the Right Side has all of our independent variables that are by themselves (usually the letter x or the letter t) and is our Particular Side. When Solving such a Differential Equation, we find the solution to each side separately (the Characteristic Solution and the Particular Solution), and then we combine them to find the General Solution for the whole problem. Given the differential equation d?y dy + 5 + 6y = 8xe-3x dx dx2 Determine the Characteristic Equation for the given Differential Equation and then find its Solutions. A Characteristic Solutions: R, = -2 and R, = -3 B Characteristic Solutions: R, -6 and R, = 2 CCharacteristic Solutions: R = -2 + /2 i Characteristic Solutions: R, = -6 and R, = 1 E Characteristic Solutions: R, 2 and R, = 3 %3D V31 (F) Characteristic Solutions: R = 5 i

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