We will have the following:
[tex]\frac{\partial y}{\partial x}=2y\Rightarrow\frac{1}{2y}\partial y=\partial x[/tex][tex]\Rightarrow\int (\frac{1}{2y})\partial y=\int \partial x\Rightarrow\frac{\log (y)}{2}=x+c[/tex]Then we find "c":
[tex]\frac{\log(1)}{2}=5+c\Rightarrow c=-5[/tex]Thus, the general solution passing through (5, 1) is:
[tex]\frac{\log(y)}{2}=x-5[/tex]