Class 12 Differential Equations · Short Answer2 Marksseparable_differential_equations
Class 12 Maths · Differential Equations · Short Answer #94
Given y′ = e^(−2y) and y(5) = 0, find x when y = 3.
✅ Step-by-Step Solution
Final Answer: x = (e⁶ + 9)/2.
- Separate e^(2y)dy = dx.
- Integrate e^(2y)/2 = x + C. At (5, 0), C = −9/2, hence e^(2y) = 2x − 9.
- At y = 3, x = (e⁶ + 9)/2; the solution domain is x > 9/2.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Separate e^(2y)dy = dx.
- [1 mark] Integrate e^(2y)/2 = x + C. At (5, 0), C = −9/2, hence e^(2y) = 2x − 9.
- [0.5 marks] At y = 3, x = (e⁶ + 9)/2; the solution domain is x > 9/2.
Master Chapter 9: Differential Equations
Practise interactive questions, flashcards, visual mind maps, and timed board tests for Differential Equations.
← Previous Question
Find an integrating factor of y′ + y = (1 + y)/x.
Next Question →Find the general solution of y′ = 2^(y−x).
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?