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2. Recall the method for Variation of Parameters for non-homogeneous equations from 4.6 notes. For Cauchy-Euler equations, a(x)y + b(x)y' + cy = f(x),
2. Recall the method for Variation of Parameters for non-homogeneous equations from 4.6 notes. For Cauchy-Euler equations, a(x)y" + b(x)y' + cy = f(x), you will solve for the auxiliary/characteristic equation as usual. Before using variation of parameters to find a particular solution, the equation needs to be written in standard form first. That is, y" needs a coefficient of 1: b(x) f(x) y" + y' + y = a(x) a(x) a(x) Now, your system of equations will be: yv'1(t) + y2v2(t) = 0 f(x) y'v'1(t)+y'v'2(t) = a(x) 5 Solve using variation of parameters: xy" +9xy' 20y= (20 pts.) x3
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