Reid's question at Yahoo Answers regarding a first order separable IVP

[MarkFL]

Here is the question:

What is the particular solution to y'x-1=0 using the inition condition x=1,y=2?

I have posted a link there to this topic so the OP can see my work.

 

[MarkFL]

Hello reid,

We are given the IVP:

$$y'x-1=0$$ where $$y(1)=2$$

Separating the variables, we obtain:

$$dy=\frac{1}{x}\,dx$$ where $$x\ne0$$

Switching the dummy variables of integration and utilizing the boundaries as limits, we obtain:

$$\int_2^{y(x)}\,du=\int_1^x\frac{dv}{v}$$

Applying the anti-derivative form of the FTOC, we find:

$$y(x)-2=\ln|x|$$

$$y(x)=\ln|x|+2$$