NCERT Class 12 · Ch 9 Exercise 9.2 · Q9
NCERT Class 12 Maths · Chapter 9 Differential Equations · Exercise 9.2 Question 9
Verify x+y=tan⁻¹y; y²y′+y²+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: Verified where a differentiable y(x) branch exists.
- Differentiate: 1+y′=y′/(1+y²).
- Multiply by 1+y² and rearrange to get y²y′+y²+1=0. At y=0 the implicit curve has no finite y′.
Master Chapter 9: Differential Equations
Practise interactive questions, flashcards, visual mind maps, and timed board tests for Differential Equations.
← Previous Question
Verify y−cos y=x; (y sin y+cos y+x)y′=y.
Next Question →Verify y=\(\sqrt{a^{2} - x^{2}}\) solves x+yy′=0, −a<x<a, y≠0.
Related Questions in Differential Equations
Class 12 Differential Equations · Mcq Single Correct
Find the degree of x²y″ = (xy′ − y)³.
Class 12 Differential Equations · Mcq Single Correct
Find the degree of y″ + 3(y′)² = x² ln(y″).
Class 12 Differential Equations · Mcq Single Correct
Find the order and degree of [1 + (y′)²]² = y″.
Class 12 Differential Equations · Mcq Single Correct
The nonconstant solutions of 2xy′ − y = 3 lie on a family of which curves?
Class 12 Differential Equations · Mcq Single Correct
Find an integrating factor of (x ln x)y′ + y = 2 ln x, for x > 0, x ≠ 1.
Class 12 Differential Equations · Mcq Single Correct
Which function satisfies (y′)² − xy′ + y = 0?