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CBSE Class 12 · 2011 · Differential EquationsLong Answer

Solve the following differential equation:

x d y + (y - x^{3}) d x = 0

Answer: $x y = \frac{x ^{4}}{4} + C$

Solution

Rearrange:

x \frac{d y}{d x} + y = x^{3}

, i.e.

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

Linear with

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

:

\frac{d}{d x} (x y) = x \cdot x^{2} = x^{3} \Rightarrow x y = \frac{x ^{4}}{4} + C

x y = \frac{x ^{4}}{4} + C

CBSE Class 12 Board · 2011 · Subjective

Practise more: all CBSE board PYQs on Differential Equations →

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