Class 12 Differential Equations · Short Answer2 Marksseparable_differential_equations
Class 12 Maths · Differential Equations · Short Answer #95
Find the general solution of y′ = 2^(y−x).
✅ Step-by-Step Solution
Final Answer: 2^(−x) − 2^(−y) = C, on real branches.
- Separate 2^(−y)dy = 2^(−x)dx.
- Integrate −2^(−y)/ln 2 = −2^(−x)/ln 2 + C₁.
- Thus 2^(−x) − 2^(−y) = C. Equivalently y = −log₂(2^(−x) − C), with 2^(−x) − C > 0.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Separate 2^(−y)dy = 2^(−x)dx.
- [1 mark] Integrate −2^(−y)/ln 2 = −2^(−x)/ln 2 + C₁.
- [0.5 marks] Thus 2^(−x) − 2^(−y) = C. Equivalently y = −log₂(2^(−x) − C), with 2^(−x) − C > 0.
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