问题
已知:$f_{1}(x)$ $g_{1}(y)$ $\mathrm{d} x$ $+$ $f_{2}(x)$ $g_{2}(y)$ $\mathrm{d} y$ $=$ $0$
是一个可分离变量的方程,则以下对该方程的变量分离结果,正确的是哪个?
选项
[A]. $\frac{f_{1}(x)}{f_{2}(x)}$ $\mathrm{d} x$ $+$ $\frac{g_{1}(y)}{g_{2}(y)}$ $\mathrm{d} y$ $=$ $0$[B]. $\frac{f_{1}(x)}{f_{2}(x)}$ $\mathrm{d} x$ $+$ $\frac{g_{2}(y)}{g_{1}(y)}$ $\mathrm{d} y$ $=$ $1$
[C]. $\frac{f_{1}(x)}{f_{2}(x)}$ $\mathrm{d} x$ $-$ $\frac{g_{2}(y)}{g_{1}(y)}$ $\mathrm{d} y$ $=$ $0$
[D]. $\frac{f_{1}(x)}{f_{2}(x)}$ $\mathrm{d} x$ $+$ $\frac{g_{2}(y)}{g_{1}(y)}$ $\mathrm{d} y$ $=$ $0$