NCERT Class 12 · Ch 9 Miscellaneous Exercise · Q8
NCERT Class 12 Maths · Chapter 9 Differential Equations · Miscellaneous Exercise Question 8
Solve y e^(x/y)dx=[x e^(x/y)+y²]dy, y≠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: \(- y + e^{\frac{x}{y}}\) = C.
- Use x=vy and dx=vdy+y dv. Substitution cancels vy eᵛdy on both sides, leaving y²eᵛdv=y²dy, hence eᵛdv=dy.
- Integrate eᵛ=y+C, hence e^(x/y)−y=C.
- Differentiate the resulting relation to recover the equation on intervals where the original expressions and the required slope are defined.
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