NCERT Class 12 · Ch 9 Exercise 9.3 · Q12
NCERT Class 12 Maths · Chapter 9 Differential Equations · Exercise 9.3 Question 12
Solve x(x²−1)y′=1, y(2)=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: \(\frac{\log{\left(\frac{x^{2} - 1}{x^{2}} \right)}}{2} - \frac{\log{\left(\frac{3}{4} \right)}}{2}\), x>1.
- Use 1/[x(x²−1)]=−1/x+x/(x²−1).
- Integrate y=−log|x|+(1/2)log|x²−1|+C.
- At x=2, C=−(1/2)log(3/4), giving the displayed solution on x>1.
- Differentiate the resulting relation to recover the equation on intervals where the original expressions and the required slope are defined.
Master Chapter 9: Differential Equations
Practise interactive questions, flashcards, visual mind maps, and timed board tests for Differential Equations.
← Previous Question
Solve (x³+x²+x+1)y′=2x²+x, y(0)=1.
Next Question →Solve cos(y′)=a, a∈R, with y(0)=1.
All Questions in Differential Equations — Exercise 9.3
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?