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Slide 1 Cauchy-Euler Equations Differential Equations Section 4.7 Slide 2 Standard Form of a CauchyEuler Equation an x n y ( n ) an 1 x n 1 y ( n 1) a2 x 2 y a1 xy a0 y g ( x) We will try to find a solution of the form y xm Slide 3 Case I m1 and m2 are distinct real roots The solution has the form y c1 x m1 c2 x m2 Example: #6 Slide 4 Case II m1 and m2 are repeated real roots The solution looks like y c1 x m1 c2 x m1 ln x Example: #2 Slide 5 Case III m1 and m2 are conjugate complex roots The solution looks like y x c1 cos( ln x) c2 sin( ln x) Example: # 14 Slide 6 Higher Order Equations Extend the form of the solution as we did for equations with constant coefficients. Refer to the top of page 196 if necessary.