Second-Order Differential Equations

Solution 1 ¬ . A homogeneous linear equation of the second order has the general form

2( ) c + 1( ) + 0( ) = 0. (1)

Let 0 = 0( ) be a nontrivial particular solution ( 0 ­ 0) of this equation. Then the general solution of equation (1) can be found from the formula:

= 0 XBT 1 + T 2 Q =

2 0 Sff ;] , where A = Q

2 Sff . (2)

For specific equations described below in 2.1.2-2.1.9, often only particular solutions are given, while the general solutions can be obtained with formula (2) (see also Paragraph 0.2.1-1, Item 3 ¬ ).