NCERT Class 12 · Ch 9 Exercise 9.4 · Q14
NCERT Class 12 Maths · Chapter 9 Differential Equations · Exercise 9.4 Question 14
Solve y′−y/x+cosec(y/x)=0 with y(1)=0.
💡 Concept Hints
- Identify the domain and the inner and outer functions, or the relevant one-sided limits.
- Apply the appropriate differentiation or limit rule, keep all chain factors, and check exceptional points.
✅ Step-by-Step Solution
Final Answer: No classical solution satisfies the printed initial condition.
- At the required initial point, y/x=0 and cosec 0 is undefined. The differential equation has no value there.
- Formal separation gives cos(y/x)=log|x|+C and the initial value would give C=1, but this formal relation cannot satisfy the original differential equation at (1,0).
- A curve defined only on one side and tending to (1,0) is not a classical solution on an interval containing the initial point.
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