Question

Solution of the differential equation Xdy - Ydx = 0 represents

• A. A rectangular hyperbola
• B. A straight line passing through the origin
• C. Parabola whose vertex is at the origin
• D. Circle whose center is at the origin

Hint:

Differential equations can be solved by separating variables and integrating both sides to find the general solution.

Answer 1

The Correct Option is B

Step 1: Understanding the given differential equation. 
The given differential equation is Xdy − Ydx = 0. We can rewrite it as: dy/dx = Y/X This represents the slope of the curve at any point on it. 

Step 2: Solution of the differential equation. 
The equation can be solved using the method of separation of variables: dy/Y = dx/X Integrating both sides: ln |Y| = ln |X| + C This simplifies to: Y = kX (where k = e^C is a constant) This is the equation of a straight line passing through the origin.

Step 3: Conclusion. 
Thus, the solution of the differential equation is a straight line passing through the origin. 

Final Answer: A straight line passing through the origin.