Question

Find the general solution to dy/dx = 2y passing through the point (5, 1)

Answer 1

We will have the following:

`(\partial y)/(\partial x)=2y\Rightarrow(1)/(2y)\partial y=\partial x`
`\Rightarrow\int ((1)/(2y))\partial y=\int \partial x\Rightarrow(\log (y))/(2)=x+c`

Then we find "c":

`(\log(1))/(2)=5+c\Rightarrow c=-5`

Thus, the general solution passing through (5, 1) is:

`(\log(y))/(2)=x-5`