Reduction of Order
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Reduction of order is a technique in mathematics for solving second-order ordinary differential equations. It is employed when one solution y1(x) is known and a second linearly independent solution y2(x) is desired. Consider the general second-order constant coefficient ODE a y''''(x) + b y''(x) + c y(x) = 0, ; where a,b,c are real non-zero coefficients. Furthermore, assume that the associated characteristic equation a lambda^{2} + b lambda + c = 0 ; has repeated roots (i.e. the discriminant, b2 4ac, vanishes).…mehr

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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Reduction of order is a technique in mathematics for solving second-order ordinary differential equations. It is employed when one solution y1(x) is known and a second linearly independent solution y2(x) is desired. Consider the general second-order constant coefficient ODE a y''''(x) + b y''(x) + c y(x) = 0, ; where a,b,c are real non-zero coefficients. Furthermore, assume that the associated characteristic equation a lambda^{2} + b lambda + c = 0 ; has repeated roots (i.e. the discriminant, b2 4ac, vanishes).