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y = 2 sin2x - 5 cos2x, prove that d2y/dx2 + 4y = 0 |
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Answer» y = 2sin 2x – 5cos 2x Differentiate y w.r.t x, we get \(\frac{dy}{d\mathrm x}\) = 4cos 2x + 10sin 2x Differentiate \(\frac{dy}{d\mathrm x}\) w.r.t x, we get \(\frac{d^2y}{d\mathrm x^2}\) = –8sin 2x + 20 cos2x = –4(2 sin2x – 5cos2x) = –4y ⇒ \(\frac{d^2y}{d\mathrm x^2}\) + 4y = 0 Hence proved |
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