求全微分方程(3x²+6xy²)dx+(6x²y+4y²)dy=0的通解.用曲线积分解答!
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/30 10:16:54
![求全微分方程(3x²+6xy²)dx+(6x²y+4y²)dy=0的通解.用曲线积分解答!](/uploads/image/z/7079815-55-5.jpg?t=%E6%B1%82%E5%85%A8%E5%BE%AE%E5%88%86%E6%96%B9%E7%A8%8B%EF%BC%883x%26%23178%3B%2B6xy%26%23178%3B%29dx%2B%286x%26%23178%3By%2B4y%26%23178%3B%29dy%3D0%E7%9A%84%E9%80%9A%E8%A7%A3.%E7%94%A8%E6%9B%B2%E7%BA%BF%E7%A7%AF%E5%88%86%E8%A7%A3%E7%AD%94%21)
求全微分方程(3x²+6xy²)dx+(6x²y+4y²)dy=0的通解.用曲线积分解答!
求全微分方程(3x²+6xy²)dx+(6x²y+4y²)dy=0的通解.
用曲线积分解答!
求全微分方程(3x²+6xy²)dx+(6x²y+4y²)dy=0的通解.用曲线积分解答!
(3x²+6xy²)dx+(6x²y+4y²)dy=0
分组得:3x²dx+(6xy²dx+6x²ydy)+4y²dy=0
即:d(x^3)+d(3x²y²)+d(4y^3/3)=0
x^3+3x²y²+4y^3/3=C