Changes

'''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:

7. The solution is then <math>y = c_1 y_1 + c_2 y_2 = e^{\lambda t} (c_1 + c_2 t)</math>

7. The solution is then <math>y = c_1 y_1 + c_2 y_2 = e^{\lambda t} (c_1 + c_2 t)</math>

[[Category: Differential Equations]]

[[Category:Differential Equations]]