Question

The solution of the $\frac{\mathrm{dy}}{\mathrm{dx}}=\frac{1}{\mathrm{x}}$is

• A. $\mathrm{y}+\log \mathrm{x}+\mathrm{c}=0$
• B. $\mathrm{y}=\log \mathrm{x}+\mathrm{c}$
• C. ${\mathrm{y}}^{\mathrm{logx}}+\mathrm{c}=0$
• D. None of these

Answer 1

The correct option is B

$\mathrm{y}=\log \mathrm{x}+\mathrm{c}$

The explanation for the correct answer.

Find the solution for the given equation:

Given: $\frac{\mathrm{dy}}{\mathrm{dx}}=\frac{1}{\mathrm{x}}$

Integrate the given equation

$$\begin{gathered} \Rightarrow \int \frac{\mathrm{dy}}{\mathrm{dx}}=\int \frac{1}{\mathrm{x}}\mathrm{dx} \\ \Rightarrow \mathrm{y}=\mathrm{logx}+\mathrm{C}\left[\int \frac{1}{\mathrm{x}}\mathrm{dx}=\mathrm{logx}+\mathrm{C}\right] \end{gathered}$$

Hence option $B$ is the correct answer.