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CBSE Class 12 · 2007 · Differential EquationsLong Answer

Solve the following differential equation:

\frac{d y}{d x} + 2 y = 6 e^{x}

Answer: $y = 2 e^{x} + C e^{- 2 x}$

Solution

Linear with

P = 2

, so

I.F. = e^{2 x}

.

\frac{d}{d x} (y e^{2 x}) = 6 e^{x} \cdot e^{2 x} = 6 e^{3 x} \Rightarrow y e^{2 x} = 2 e^{3 x} + C

y = 2 e^{x} + C e^{- 2 x}

CBSE Class 12 Board · 2007 · Subjective

Practise more: all CBSE board PYQs on Differential Equations →

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