Separation of variables Calculus The given differential equation I need to solve is $dy/dx=1/x$ with the initial conditon of $x=1$ and $y=10$
My attempt: 
$dy=\frac 1x dx$
Integrating yields 
\begin{align*} 
   y&=\log x+C\\
   x=1 & y=10\\
 10 &=\log 1 + C\\
  10=C\\
\leadsto y&=\log x+10
\end{align*}
Something seems off with my work, if anyone could give me a clue where I went wrong. Thanks

We have $$\frac{\mathrm{d}y}{\mathrm{d}x} = \frac{1}{x}$$ Hence, separating the variables gives us $$\int \mathrm{d}y = \ln x + c \implies y=\ln x + c.$$ Using the initial condition of $x=1, y=10$ gives us $$10 = 0 + c \iff c = 10.$$ So the solution is $$\bbox[10px, border: solid lightblue 2px]{y = \ln x + 10}$$ which is exactly what you got and is correct! 

To verify your answer, you can see that when $x=1$, you get $y=10$ and differentiating your answer results in $$\frac{\mathrm{d}y}{\mathrm{d}x} = \frac{1}{x},$$ which is what you were given at the beginning. 
