解法 1 解特征方程[tex=3.429x1.357]TTB+A2BMH0X5MHsq7ogkCw==[/tex]，得[tex=2.143x1.214]KbyaOQYU3kJ4H4SYax9A6Q==[/tex]，[tex=2.857x1.214]IcGrHSH71BAqVlePjAg9Ng==[/tex]，故对应的齐次方程的通 解为[tex=7.0x1.429]V1s9agDEpFlg2wyzt3w4tMoavGtc9jC1JojjZXqcyMnk513u4qrWY3jvVtfPp+to[/tex]这里[tex=3.643x1.5]KRHxTTiXOfq8Chhy1w9tZg==[/tex]，由于[tex=2.429x1.0]tv0/A0DlvArlnDLq6FCi6g==[/tex]是特征方程的单根，故可设[tex=14.214x1.571]UW3A7k6qZCOPDHyt2XcdBaTWLp0yYMaatkHaleSac+hr6CfcCjwIDHBbePbUeULzpw3vy+qiYNAvmBmAAGjtaA==[/tex]是原方程的一个特解，代入原方程并化简得[tex=11.357x1.5]eAFvoUYfH5Q9Men6SmKjfFsgAi7lX6C4Ks0PvYTuZXIkIurgRyd6VPzidksr7DDK[/tex]，比较同次幂的系数，得[tex=5.929x3.929]fnpmC2J6JmQBLyo5NmGAz4zt3y6vzskwOlrc+qIKpH2LGXCB93jPYLR2vI/tGcvPDtq8kv+twKpjzzBzuz4f1X2lTXH67l0Oy4DqUjxpHbg=[/tex]解之得[tex=4.429x5.214]fnpmC2J6JmQBLyo5NmGAz3pKuOA6ldzjNyDjDbsy2LflmGQOkSA8fnpi4eY1n6cZmvJ6XuZdwY6kpBVM0CM8qtTbBbVmkZ0drlU4sVqFaH0=[/tex][tex=6.929x2.357]v2O51jSMJsAVDrVYMTj/ad5/3yvOS6E3mGv5Hp4/XWs=[/tex]，原方程的通解为[tex=11.857x2.357]wpELuy8TWjHIs/nFNv9v5cQnX6GF3wQZVzVNQiIx1ViYIcq/aqVMPBxfXWfZwOgBBYZCYe5U5kpRJJC1exRoLQ==[/tex].解法 2 令[tex=2.071x1.357]dd5WXHgntCws1vGEnzXOtg==[/tex]，则[tex=2.5x1.357]rjzw0bBUODiY66l+Mq83xE2Kmm9Gx2OjSuXrHQFQSgA=[/tex]，原方程化成[tex=3.786x1.429]ba6zPjYqsxQ/tIObAzvD1eN7QhJ3mbDyhB4pEJ00lWw=[/tex]，于 是[tex=12.286x8.714]eQ6UQYQ/W2A+qqbp78q83UBh+IH57qgXOpzzHB6YZFBabzSTgrP12fqZ/UliH7C7yh/XowHKeauWA7h8tS0HBT3TJWx6/w9OKKFUIb0FN8+7AyMVW96kjHsr6eG0/SBV/Q8hr//WFFoCwDIoEj5O4lFUgTeOFO8thn5J+WPisrnL0+rVeFKPIFyt1Owd/yASw0hTruad71c/lATtCLAIuh1QcUYpZG5mzQq/lBBv//EvU6llV0FVmCttXL+BCEaKSLCVQNlaXTbEKdbKfdToFn6PSrI2kuYq+8wpfFUvBL08sNGV3qlpa1Hf1oCZUqHMo+Z+RzEH2F0IEvcDftSTIpIh/ZdVqUuf6VGb63eBKT64nPFmtGE7/gQxzGmYj6EY027L9L9vkP/61YC6MlpEqJujmdxo3EZMFVNDTjb0vZQ=[/tex]即[tex=8.929x1.429]PJShe/1uQDG3R1HReKlO7XXHULVZEuz+Fa7C3MjkRveNshq4gbgfM9MIVxL4LzQT[/tex]，两端积分，得[tex=11.857x2.357]5qkJaXqSAKsrC7IU/csmhy8W6YRvubrksy2RXZ9Z62u69WMz0nd6glo/g4obaUSpS2aRpS31LimYUwyMQl/7VQ==[/tex].