解 该方程对应的齐次方程为[tex=3.5x1.357]rjzw0bBUODiY66l+Mq83xJhzkPUn1E4gGAfeHRIb5kk=[/tex]. 齐次方程对应的特征方程为 [tex=3.571x1.357]YMeb5av17aGhHM+RcbJJP3IgSXMp4eQB9UHd6aI5WKI=[/tex], 特征根为[tex=2.929x1.143]e1WJqAgnmQmd3yoMqAMyN1llNnBZzPRwMBqzT/ACkaM=[/tex].故齐次方程的通解为[tex=8.0x1.214]QnyYMeaE+t3uRKFVssFDGd/hn+Uff8FPbkcHYb9RFfk=[/tex].将此通解中的任意常数[tex=2.071x1.0]tvDfEv4OKQqfas/giCADwQ==[/tex]分别变易为侍定函数 [tex=4.714x1.357]7oSF4i8Gpeg9oWWlpCLjubwsFHbRDRlxm91qNoPYIAM=[/tex], 联立解方程组[tex=14.286x3.357]7EJHVCtO2IWq3KpdB+jQsocafjfWbJKaWEt3X+to5sYzoo3FWKfDbfytNjqXGF0okoyYn2eZCEiFobbcS7/6g1dTFQmdPtxHP1oZf/KavghwSQ9dymFWW30h6razo+FeCHcm4sVSbyjRjuyxMddpeNd70zc88GhuCsTZsQggqGiK2sFY5VAkUhx3T1UrFZS8Sr2LNBTATVszAZ6tW+IQ+WXsaRN8zIGzw3vjOeOCV0A=[/tex]得[tex=8.143x3.357]7EJHVCtO2IWq3KpdB+jQspAfBKEwOrbhqOZ8qeKBW0qyI/CUV2x6Nsd/G/ZuDuhd/ri64JfVsX2JjyrD/Jcr3CDzVaZfFNChpEaYNmJAZu2wqARdiLUWRkQJqhCr+RkdDyLt3tt8NNmFseJox85mcA==[/tex]积分后,取 [tex=10.786x3.357]7EJHVCtO2IWq3KpdB+jQsnDRZuLEcwoKWOqnhFsWR+jXppom4rGdbIzWI1GR/pHgZTRb6H7ZCcpRmKm/7gwK8oouelIxNAhou7RpFlM++oixglDN/e/KySzkWt9IhIDGvTCo5iISBGdrxHAWEFIM9g==[/tex]于是获得非齐次方程的一个特解[tex=19.429x1.357]8KnVCZvrZAv+CPswi1Hh+rrn1jwCWgIDAvJzvfVfiY8YT4lUXFB4p+7AGJNYa/JhgwSwmA2LdEJxKxj4eTbAtvmSI08/HX0wvfpAK9kSTvY=[/tex]合并同类项,得[tex=1.857x1.214]TIlgh23OSOlH4wSn00DZmw==[/tex], 最后得到方程[tex=3.571x1.357]rjzw0bBUODiY66l+Mq83xNiOoJfkieX/GLipkFlJjeM=[/tex]的通解为[tex=9.357x1.214]QnyYMeaE+t3uRKFVssFDGcLIOJ2NFbg3aFb7n6jvqSr2PnB4c1yvfAR7CBiZ7pFy[/tex].