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