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CBSE Class 12 · 2009 · Differential EquationsLong Answer

Find the particular solution of the differential equation

\frac{d y}{d x} + y cot x = 4 x cosec x, (x \neq = 0)

, given that

y = 0

when

x = \frac{π}{2}

.

Answer: $y sin x = 2 x^{2} - \frac{π ^{2}}{2}$

Solution

Linear with

P = cot x

.

I.F. = e^{\int c o t x d x} = e^{l o g ∣ s i n x ∣} = sin x

y sin x = \int 4 x cosec x \cdot sin x d x = \int 4 x d x = 2 x^{2} + C

Apply

y = 0

at

x = \frac{π}{2}

:

0 = 2 \cdot \frac{π ^{2}}{4} + C \Rightarrow C = - \frac{π ^{2}}{2}

.

y sin x = 2 x^{2} - \frac{π ^{2}}{2}

CBSE Class 12 Board · 2009 · Subjective

Practise more: all CBSE board PYQs on Differential Equations →

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