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प्रश्न
If y = 2 sin x + 3 cos x, then show that y2 + y = 0.
उत्तर
Given y = 2 sin x + 3 cos x ....(1)
Differentiating with respect to 'x' we get,
y1 = 2 cos x - 3 sin x
Differentiating again with respect to 'x' we get,
y2 = 2 (- sin x) - 3 cos x
y2 = - 2 sin x - 3 cos x ....(2)
Adding (1) and (2) we get,
y + y2 = 2 sin x + 3 cos x - 2 sin x - 3 cos x
= 0
y + y2 = 0
Hence proved.
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