CBSE BoardEnglish MediumSTD 12 ScienceApplied MathsDifferential Equations and Modeling2 Marks
Question
Find the general solution of the differential equation $\frac{d y}{d x}=e^{x+y}$
✓
Answer
Given differential equation is $\frac{d y}{d x}=e^{x+y}$ $\Rightarrow \quad \frac{d y}{d x}=e^x e^y$ $\Rightarrow \quad \frac{d y}{e^y}=\left(e^x\right) d x$ $\Rightarrow \quad\left(e^{-y}\right) d y=\left(e^x\right) d x$ Integrating both sides, we get $\int\left(e^{-y}\right) d y=\int\left(e^x\right) d x$ $\Rightarrow \quad-e^{-y}=e^x+c^{\prime}$ $\Rightarrow \quad e^{-y}=-e^x+c[$ where $c=-\dot{c}$
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