KCET · Maths · Differential Equations
The solution for the differential equation \( \frac{d y}{y}+\frac{d x}{x}=0 \)
- A \( \frac{1}{y}+\frac{1}{x}=C \)
- B \( \log x \cdot \log y=c \)
- C \( x y=c \)
- D \( x+y=c \)
Answer & Solution
Correct Answer
(C) \( x y=c \)
Step-by-step Solution
Detailed explanation
Given differential equation is,
\( \frac{d y}{y}+\frac{d x}{x}=0 \)
Integrating both the sides
\[
\begin{array}{l}
\int \frac{d y}{y}+\int \frac{d x}{x}=\int \operatorname{Od} x \\
\Rightarrow \log y+\log x=\log c \\
\Rightarrow \log (x y)=\log c \\
\Rightarrow x y=c
\end{array}
\]
\( \frac{d y}{y}+\frac{d x}{x}=0 \)
Integrating both the sides
\[
\begin{array}{l}
\int \frac{d y}{y}+\int \frac{d x}{x}=\int \operatorname{Od} x \\
\Rightarrow \log y+\log x=\log c \\
\Rightarrow \log (x y)=\log c \\
\Rightarrow x y=c
\end{array}
\]
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