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CBSE Class 12 · 2011 · Differential EquationsLong Answer

Solve the following differential equation:

e^{x} tan y d x + (1 - e^{x}) sec^{2} y d y = 0

Answer: $tan y = C (1 - e^{x})$

Solution

Separate variables:

\frac{sec ^{2} y}{tan y} d y = \frac{- e ^{x}}{1 - e ^{x}} d x

Each side is a

\frac{f ^{'}}{f}

form. Integrating:

lo g ∣ tan y ∣ = lo g ∣1 - e^{x} ∣ + lo g C

tan y = C (1 - e^{x})

CBSE Class 12 Board · 2011 · Subjective

Practise more: all CBSE board PYQs on Differential Equations →

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