NCERT Class 12 · Ch 9 Miscellaneous Exercise · Q1
NCERT Class 12 Maths · Chapter 9 Differential Equations · Miscellaneous Exercise Question 1
Give order and degree: (i) y″+5x(y′)²−6y=log x; (ii) (y′)³−4(y′)²+7y=sin x; (iii) y⁽⁴⁾−sin(y‴)=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: (i) order 2, degree 1; (ii) order 1, degree 3; (iii) order 4, degree undefined.
- Identify the highest derivative: second, first and fourth, respectively.
- For the polynomial equations, the highest-order derivative powers are 1 and 3. The sine of a derivative in (iii) prevents a defined degree.
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