CBSE BoardEnglish MediumSTD 12 ScienceApplied MathsDifferential Equations and Modeling2 Marks
Question
Write the solution of the differential equation $\frac{d y}{d x}=2^{-y}$
✓
Answer
Given differential equation is $\frac{d y}{d x}=2^{-y}$ On separating the variables, we get $2^y d y=d x$ On integrating both sides, we get c $\int 2^y d y=\int d x$ or $\frac{2^y}{\log 2}=x+C_1$ or $2^y=x \log 2+C_1 \log 2$ $\therefore 2^y=x \log 2+C$, where $C=C_1 \log 2$
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