NCERT Class 12 · Ch 9 Exercise 9.4 · Q10
NCERT Class 12 Maths · Chapter 9 Differential Equations · Exercise 9.4 Question 10
Show (1+e^(x/y))dx+e^(x/y)(1−x/y)dy=0 is homogeneous and solve.
💡 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: x+y e^(x/y)=C, y≠0.
- Both coefficients depend only on x/y, so the differential equation is homogeneous.
- It is also exact: d[x+y e^(x/y)]=(1+e^(x/y))dx+e^(x/y)(1−x/y)dy. Hence the bracket is constant.
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