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CBSE Class 12 · 2015 · Differential EquationsVery Short Answer

Find the integrating factor of the differential equation

(\frac{e ^{- 2 x}}{x} - \frac{y}{x}) \frac{d x}{d y} = 1

.

Answer: $e^{2 x}$

Solution

Rewrite with

\frac{d y}{d x}

. Since

\frac{d x}{d y} = (\frac{e ^{- 2 x}}{x} - \frac{y}{x})^{- 1}

, we get

\frac{d y}{d x} = \frac{e ^{- 2 x}}{x} - \frac{y}{x} \Rightarrow \frac{d y}{d x} + \frac{1}{x} y = \frac{e ^{- 2 x}}{x}

This is linear with

P = \frac{1}{x}

, so

I.F. = e^{\int x^{- 1/2} d x} = e^{2 x}

I.F. = e^{2 x}

CBSE Class 12 Board · 2015 · Subjective

Practise more: all CBSE board PYQs on Differential Equations →

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