解：一阶线性非齐次方程[tex=7.857x1.286]Mm8QLH4XLrrzIdt/5/uGH2ZA7CZooL6oMeetEZW0Gro=[/tex]①的通解由两项构成，第一项[tex=4.643x1.286]m9WgF3IfUKuR/ZcDwlj2c0jTyZzAxAmIXrHiAUrSW8X29M4dPfmJH0M8kQ07GNyx[/tex]是对应齐次方程[tex=5.357x1.429]wZ5SkXcFZoyDR3r8rXMHUZm/6WDO4VJFIdwANvY7uYA=[/tex]的通解；第二项[tex=12.786x2.857]fgisHDoR5uQxJHW2TeHZFiSLXVyPcesFGMEgp38fTKICcCkFVDjiLPqa5uhE1XSXu0MwNYPIsWbnOF9EUEun5bNPTaGraJWK5BbnQb9StTY=[/tex]是原非齐次方程的一个特解（通解中[tex=2.571x1.286]ZsW2s/3Wj6gdg0gy5t5nyw==[/tex]即是它）。方程①的通解公式推导如下：（1）求①对应的齐次方程[tex=5.357x1.429]wZ5SkXcFZoyDR3r8rXMHUZm/6WDO4VJFIdwANvY7uYA=[/tex]的通解，这不难用分离变量法得到[tex=5.929x1.5]rse/svbhCqG73CLOBS2xwQsV/JRPW4eFy0mmCIC5gwjUHLBgWJrygGdwdlly3Wb0[/tex]（2）设①有形如上式得通解[tex=7.286x1.571]dD1rbzKSSE/LT5ExqfhdDdrZpDrmlTn2PfZ9CVFXrOvrdOlDM/pWgrQLt5ZX+DXf[/tex]②，这里[tex=2.071x1.286]FTNOAgRq5scSV+9k4i9ZxQ==[/tex]是待定函数将②两边对[tex=0.571x1.286]XubEW9+1+hkJqH7jXe5MrA==[/tex]求导，得[tex=16.643x1.571]taFK9dd87ivs9knOYdJS4FzO8+X+QbQvR+iBUJDRR69NJyypjjGVle5997yEpl601rv4ggwLLueOwTaR+7hJ3gMWSOdmIOq0YC2XOUTtARi27U27n4vNec/r0r8MdbJb[/tex]把[tex=0.571x1.286]Hz6y44ELFVLLNrLVhO3CQA==[/tex]，[tex=0.786x1.286]q2wvJrzo9GG+DZQ6l2g1dQ==[/tex]代入方程①，得[tex=15.5x1.571]b8HB8jBmMkxVPJ6Lsf0Je6tPU++NulSimZyXrSYO8ych9mWBJFDqBwf/aBy8IJlS/RoZFMkTKUmM5mgc7MFU8/+9jp6Ie1ED7FTEs5QVttrSkCIbKiZJdXImCtAOD1XA[/tex][tex=10.714x1.571]mRNVjhDmNN2r8W7TkE2WRzhOiuPkqPjqCTpE9V1y4AqzFXa+3BfZwwV0pzS5BKfM[/tex]即[tex=9.143x1.571]b8HB8jBmMkxVPJ6Lsf0Je6tPU++NulSimZyXrSYO8ycJBI4bowruBD/4fW2B7eIbeyl3BFTsSvKKPoE1/zOIWQ==[/tex][tex=8.5x1.571]b8HB8jBmMkxVPJ6Lsf0Je8xddLY5FZH2mwYZxaIzb/kNjh8ZkFWitIg3R9qOslnSHHoMbzfdvCaN5dRCcXuDpg==[/tex]故有[tex=12.143x2.643]fG4DNdk1erEIBeM/MGFzEbwkPK+vJD1aQ0fHzzvOIdmTSNdji3ULXJcKi4NhDnJVJhqzE4ZQv86/LpmrXNLauw==[/tex]从而得到一阶线性非齐次微分方程①的通解[tex=15.643x2.786]EDgxX48HQTCJ/D1KjB/1wPIOtBEo2fadp0AA4gskDJAaf/UYvgXd+ECPx3S55+9fUrRx4cgs7/Y+4UImoXW2mXYVbVSF1ciKcelHYiihZVrmY76fGQpYhPmfZRMsZ22B[/tex]即[tex=10.429x1.5]rse/svbhCqG73CLOBS2xwcuDYBizTe6xWuLsKabYl3NMKJgufXjRC55lyfcLp+eKtIoFZSpto3eIDpcuU5Zm9A==[/tex][tex=7.643x2.643]JuWFr+mMMnvW/stS9aL7+OjYS6acbpbT6Mx7CIutYIH3lUGXJZNYTQUyGSAgzsjX4eDKbFfhPgk9WlRg9mbv6w==[/tex]。