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CBSE Class 12 · 2019 · Differential EquationsLong Answer

Solve the differential equation

x \frac{d y}{d x} = y - x tan (\frac{y}{x})

.

Answer: $x sin (\frac{y}{x}) = C$

Solution

Write

\frac{d y}{d x} = \frac{y}{x} - tan \frac{y}{x}

(homogeneous). Put

y = v x

:

v + x \frac{d v}{d x} = v - tan v \Rightarrow cot v d v = - \frac{d x}{x}

lo g ∣ sin v ∣ = - lo g ∣ x ∣ + lo g C \Rightarrow x sin v = C

With

v = \frac{y}{x}

:

x sin (\frac{y}{x}) = C

CBSE Class 12 Board · 2019 · Subjective

Practise more: all CBSE board PYQs on Differential Equations →

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