The general solution of the differential equation x dy − y dx = 0 represents:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → straight line passing through origin
The equation is variables separable:
\(x\,dy = y\,dx\)
\( \displaystyle \frac{dy}{y} = \frac{dx}{x} \)
Integrating both sides:
\(\log|y| = \log|x| + \log|c|\)
\(y = cx\)
For every value of c, y = cx is a straight line through the origin (with slope c).
NCERT Exemplar:
Differential Equations
