NCERT Class 12 · Ch 9 Exercise 9.3 · Q8
NCERT Class 12 Maths · Chapter 9 Differential Equations · Exercise 9.3 Question 8
Solve x⁵y′=−y⁵.
💡 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: 1/y⁴+1/x⁴=C for nonzero y, plus y=0; x≠0.
- For nonzero x,y, separate y^(−5)dy=−x^(−5)dx.
- Integrating gives −1/(4y⁴)=1/(4x⁴)+C, or 1/y⁴+1/x⁴=C.
- The solution y=0 was lost by division and must also be included. Nonzero real branches require C−1/x⁴>0.
- Differentiate the resulting relation to recover the equation on intervals where the original expressions and the required slope are defined.
Master Chapter 9: Differential Equations
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All Questions in Differential Equations — Exercise 9.3
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