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CBSE Class 12 · 2022 · Differential EquationsShort Answer

Find the general solution of the following differential equation:

\frac{d y}{d x} = e^{x - y} + x^{2} e^{- y}

Answer: $e^{y} = e^{x} + \frac{x ^{3}}{3} + C$

Solution

Factor out

e^{- y}

on the right:

\frac{d y}{d x} = e^{- y} (e^{x} + x^{2}) \Rightarrow e^{y} d y = (e^{x} + x^{2}) d x

Integrate both sides:

\int e^{y} d y = \int (e^{x} + x^{2}) d x

e^{y} = e^{x} + \frac{x ^{3}}{3} + C

CBSE Class 12 Board · 2022 · Subjective

Practise more: all CBSE board PYQs on Differential Equations →

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