论文标题
曲线的家庭与线的正交家族$ y = mx-2m-m^3 $
Families of curves orthogonal to the lines $y=mx-2m-m^3$
论文作者
论文摘要
$ y = mx-2m-m^3 $的系列众所周知，抛物线$ y^2 = 4x $是正常的。但是，这种线条家庭正常是曲线的一系列曲线家族。在这里，通过解决有趣的一阶和三级颂歌，我们提出了这些曲线。由此产生的一组曲线是“类似抛物线的”，但非标准的曲线和另一个家庭甚至都不是“抛物线”。
The family of lines $y=mx-2m-m^3$, are well known to be normal to the parabola $y^2=4x$. However, this family of lines is normal to a family of curves of which this parabola is just one member. Here, by solving an interesting first order and third degree ODE, we bring out these curves. The resulting one set of curves are "parabola-like" but non-standard ones and the other family is not even "parabola like".
