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CBSE Class 12 · 2006 · Differential EquationsVery Short Answer

Solve the following differential equation:

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

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

Solution

This is linear in

y

with

P = - \frac{1}{x}

,

Q = 2 x^{2}

.
Integrating factor:

I.F. = e^{\int - \frac{1}{x} d x} = e^{- l o g x} = \frac{1}{x}

Then

\frac{d}{d x} (\frac{y}{x}) = 2 x^{2} \cdot \frac{1}{x} = 2 x \Rightarrow \frac{y}{x} = \int 2 x d x = x^{2} + C

y = x^{3} + C x

CBSE Class 12 Board · 2006 · Subjective

Practise more: all CBSE board PYQs on Differential Equations →

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