NCERT Class 12 · Ch 9 Exercise 9.5 · Q3
NCERT Class 12 Maths · Chapter 9 Differential Equations · Exercise 9.5 Question 3
Solve y′+\(\frac{1}{x}\) y=\(x^{2}\).
💡 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 = \(\frac{4 C + x^{4}}{4 x}\), on x>0 or x<0.
- Write y′ + \(\frac{1}{x}\) y = \(x^{2}\); work on x>0 or x<0.
- An integrating factor is μ=\(x\), since μ′/μ=\(\frac{1}{x}\).
- Multiply through: d(μy)/dx = \(x^{3}\).
- Integrate the right side: \(\frac{x^{4}}{4}\). Thus μy=\(\frac{x^{4}}{4}\)+C.
- Therefore y = \(\frac{4 C + x^{4}}{4 x}\).
Master Chapter 9: Differential Equations
Practise interactive questions, flashcards, visual mind maps, and timed board tests for Differential Equations.
← Previous Question
Solve y′+\(3\) y=\(e^{- 2 x}\).
Next Question →Solve y′+\(\sec{\left(x \right)}\) y=\(\tan{\left(x \right)}\).
All Questions in Differential Equations — Exercise 9.5
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?