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'''Reduction of order''' is a process used to find the solution of a differential equation <math>y'' + p(t)y' + q(t)y = 0</math>, when [[Euler substitution]] methods find only one value for <math>\lambda</math>. (That is, <math>\sqrt {b^2-4ac} = 0</math> and <math>\lambda = \frac{-b}{2a}</math>.)
'''Reduction of order''' is a process used to find the solution of a differential equation <math>y'' + p(t)y' + q(t)y = 0</math>, when [[Euler substitution]] methods find only one value for <math>\lambda</math>. (That is, <math>\sqrt {b^2-4ac} = 0</math> and <math>\lambda = \frac{-b}{2a}</math>.)
The process is carried out in the following manner:
The process is carried out in the following manner: