Class 12 Differential Equations · Very Long Answer5 Marksseparable_differential_equations
Class 12 Maths · Differential Equations · Very Long Answer #116
Given (y dx − xdy)/y = 0 for x, y > 0 and y(1) = 1, find y(5).
✅ Step-by-Step Solution
Final Answer: y(5) = 5.
- Convert the differential form to y − xy′ = 0, with x, y > 0.
- Separate dy/y = dx/x.
- Integrate ln y = ln x + C, so y = Ax with A > 0.
- The corrected initial condition y(1) = 1 gives A = 1.
- Therefore y = x and y(5) = 5.
📋 CBSE Stepwise Marking Scheme
- [1 mark] Convert the differential form to y − xy′ = 0, with x, y > 0.
- [1 mark] Separate dy/y = dx/x.
- [1 mark] Integrate ln y = ln x + C, so y = Ax with A > 0.
- [1 mark] The corrected initial condition y(1) = 1 gives A = 1.
- [1 mark] Therefore y = x and y(5) = 5.
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