Class 12 Differential Equations · Very Long Answer5 Markslinear_differential_equations
Class 12 Maths · Differential Equations · Very Long Answer #76
Solve cos x · y′ − y sin x = 6x, 0 < x < π/2, y(π/3) = 0, and find y(π/6).
✅ Step-by-Step Solution
Final Answer: y(π/6) = −π²/(2√3).
- Recognize the left-hand side as (y cos x)′.
- Integrating gives y cos x = 3x² + C.
- At x = π/3, y = 0 implies C = −π²/3.
- Thus y = (3x² − π²/3)sec x on (0, π/2).
- At x = π/6, y = (π²/12 − π²/3)(2/√3) = −π²/(2√3).
📋 CBSE Stepwise Marking Scheme
- [1 mark] Recognize the left-hand side as (y cos x)′.
- [1 mark] Integrating gives y cos x = 3x² + C.
- [1 mark] At x = π/3, y = 0 implies C = −π²/3.
- [1 mark] Thus y = (3x² − π²/3)sec x on (0, π/2).
- [1 mark] At x = π/6, y = (π²/12 − π²/3)(2/√3) = −π²/(2√3).
Master Chapter 9: Differential Equations
Practise interactive questions, flashcards, visual mind maps, and timed board tests for Differential Equations.
← Previous Question
A solution y = f(x) of 2x²dy = (2xy + y²)dx passes through (1, 2)…
Next Question →Solve xy′ + y − x + xy cot x = 0, x ≠ 0.
More Practice Questions in Differential Equations
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?