NCERT Class 12 · Ch 9 Exercise 9.5 · Q16
NCERT Class 12 Maths · Chapter 9 Differential Equations · Exercise 9.5 Question 16
Find the curve through the origin whose tangent slope equals the sum x+y of its coordinates.
💡 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 = \(- x + e^{x} - 1\), on intervals where the original equation is defined.
- Write y′ + \(-1\) y = \(x\); work on intervals where the original equation is defined.
- An integrating factor is μ=\(e^{- x}\), since μ′/μ=\(-1\).
- Multiply through: d(μy)/dx = \(x e^{- x}\).
- Integrate the right side: \(\left(- x - 1\right) e^{- x}\). Thus μy=\(\left(- x - 1\right) e^{- x}\)+C.
- Substitute x=\(0\), y=\(0\): C=\(1\).
- Therefore y = \(- x + e^{x} - 1\).
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