The solution curve of the differential equation \( \displaystyle\frac{x\,dy}{2\,dx}=y+9 \) represents a/an:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → Parabola
The variables separate:
\( \displaystyle \frac{dy}{y+9}=\frac{2\,dx}{x} \)
Integrating both sides:
\( \displaystyle \log|y+9|=2\log|x|+\log|C| \)
\( \displaystyle \log|y+9|=\log|Cx^2| \)
\( \displaystyle y+9=Cx^2 \)
This is \( x^2=\frac{1}{C}(y+9) \), a parabola with vertex (0, −9) and its axis along the y-axis.