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Differential Equations
NCERT Class 12
CBSE
Grade 12
Question:
Find particular solution of $\dfrac{dy}{dx} - 3y \cot x = \sin 2x$ given $y = 2$ when $x = \pi/2$.
Step-by-Step Solution
$\text{I.F.} = \csc^3 x \Rightarrow y \csc^3 x = -2\csc x + C$. [1.5 Marks] At $x = \pi/2, y = 2 \Rightarrow C = 4 \Rightarrow y = 4\sin^3 x - 2\sin^2 x$. [1.5 Marks]
--- 🎯 Official CBSE Marking Scheme: Evaluating I.F. $= \csc^3 x$: 1.5 Marks Evaluating particular solution $y = 4\sin^3 x - 2\sin^2 x$: 1.5 Marks
Correct Answer:
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