NCERT Class 12 · Ch 9 Exercise 9.5 · Q17
NCERT Class 12 Maths · Chapter 9 Differential Equations · Exercise 9.5 Question 17
Find a curve through (0,2) whose coordinate sum exceeds the magnitude of its tangent slope by 5.
💡 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: No real differentiable curve satisfies the literal printed condition.
- The condition is x+y−|y′|=5. At (0,2), it gives |y′(0)|=−3.
- A real absolute value cannot be negative. Thus the initial condition is inconsistent.
- If “magnitude” was intended to mean signed slope, the altered equation y′=x+y−5 would instead give y=4−x−2eˣ. That is an editorial alternative, not a solution of the printed condition.
Master Chapter 9: Differential Equations
Practise interactive questions, flashcards, visual mind maps, and timed board tests for Differential Equations.
← Previous Question
Find the curve through the origin whose tangent slope equals the sum…
Next Question →Find an integrating factor of xy′−y=2x².
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?