y = a \cos ( \ln x ) + b \sin ( \ln x
Lös ut a
\left\{\begin{matrix}a=-\frac{b\sin(\ln(x))-y}{\cos(\ln(x))}\text{, }&\nexists n_{1}\in \mathrm{Z}\text{ : }x=e^{\pi n_{1}+\frac{\pi }{2}}\text{ and }x>0\\a\in \mathrm{R}\text{, }&y=b\sin(\ln(x))\text{ and }\exists n_{1}\in \mathrm{Z}\text{ : }x=e^{\frac{\pi \left(2n_{1}+1\right)}{2}}\end{matrix}\right,
Lös ut b
\left\{\begin{matrix}b=-\frac{a\cos(\ln(x))-y}{\sin(\ln(x))}\text{, }&\nexists n_{1}\in \mathrm{Z}\text{ : }x=e^{\pi n_{1}}\text{ and }x>0\\b\in \mathrm{R}\text{, }&y=a\cos(\ln(x))\text{ and }\exists n_{1}\in \mathrm{Z}\text{ : }x=e^{\pi n_{1}}\end{matrix}\right,
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