上方程可化为 [tex=9.357x1.5]JKCgVm6HKZpTx4WQaZ/+XpPLckeEvjPxpwlcbGFJ6QAoLDQNTotYaAzfDQ13L/SV[/tex], 即[tex=11.643x2.571]Y5T1dtPlMS/Dx+a9nmlTh9gcm/p0ICzjO1BwgwZMsxxUyLUvA7Gm3ob7FtafoCy/jsH4Myc4PVCdweELwjNQ9g==[/tex] .显然令 [tex=2.857x1.429]SKNXKw/ScUuJuz3vcy0RRw==[/tex], 代入上方程得[tex=6.0x2.429]IrIRDjJ7T98eP9/GusyDQXqUDhE2nesoBE9+S2oRrf4=[/tex]此为一阶线性微分方程, 有[tex=25.643x4.5]qeiYnKXLEhyhuGRg8yLtrzE7yma3qu6HlutPBmKW7pAla5WQxONmDFqqxCWjRJVZ9AWbbCla3I32ZpB7EFOdHV/51lRZcpF6nGa1o0+5F8Nx5+haBVfccxBlqqGqp8PRrF/aiARlGkgbX47/mFT9hMJLPXJOTNYv8ZNcHl8pCPtiUqedPb4fRIR4tLlLCxLWNxRiOLU3gBHnyVqZvNQpsuyoT1BqrZzhRHwybs3l0MQ=[/tex]所求通解为 [tex=6.714x1.429]8LCD0z9IC1EwT65eOKwliikVhF2OLQd2LAOSXOlOH38=[/tex], 即 [tex=8.0x1.571]FeTH8qI/oUhUIDubFiTyeb2S2ye0XvvqeF+xyK1gr+n1669xwvzCp/CxJT7TwOvn[/tex] 解毕.如取 [tex=0.571x0.786]ZKO2xs0EgSemzoH7MSmYTA==[/tex] 为因变量, [tex=0.5x1.0]yBR4oiFoTexGaFalQ7m8kg==[/tex] 为自变量,同样可作代换 [tex=3.357x1.214]9RR7Ka58ZzcpvQSSIFiHKlTjOZ81w1dw1ASB9x3Bc64=[/tex] 将伯努利方程 [tex=13.214x2.214]FjQG4EbsrHEFfnCLpSg/4dWjtdkNGtrBE/czqAlGjC3cMKTEQKQe6TUgOcx0oTnJUifZMFtHMwgbf2AevV0F4Q==[/tex], 即[tex=12.0x2.214]ASELbaOCIpIHulAa/FNtLnjQv+yuOncSfvO6dkvhI9chlS503bpZaWsKDMD6YTfO075j6kuly8f+yskNLiehrA==[/tex] ,[tex=13.5x2.357]//ah+H+KvifyGyrg1OrusvfdRs8Fty9BLErOmHKEN1q9jLu79r4lapx1yBkMkX18Sk4siCgZ+81MDmkBwwbfr05WKvdmKZdgSJ9/sWzj8SE=[/tex]化为新变量 [tex=0.643x0.786]dFKQavWFzybe6S1GPVXNhQ==[/tex] 的一阶线性方程:[tex=10.286x2.643]YBBsDsJeyq4Z7N/KByrGYHcdwuYk0141b3X5wpSqtO0NCoQXk33dWSZn7IqiS6FSEXeCel7qvN+C/JcHmL5n1g==[/tex] 即 [tex=13.357x2.643]Q144bPvwHPvf5kivTpZS8YCz1lY6OKf7zhxWWhYW3PgTQQiAdf/ZU3zhhDBIMyU6gcXhqXPrdQ53ES6PaCiKRw==[/tex]