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If y = ex (sin x + cos x), then show that \(\frac{d^2y}{dx^2}-2\frac{dy}{dx}+2y=0\)

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Given,

y = ex (sin x + cos x)

+1 vote
by (50 points)

Since y = e(sinx + cosx)

dy/dx = e(sinx + cosx) +e(cosx - sinx)

dy/dx = y + e(cosx - sinx)

d2y/ dx= dy/dx + e(cosx - sinx) +ex(-sinx - cosx)

d2y/dx= dy/dx + dy/dx - y - y

d2y/dx= 2dy/dx -2y

d2y/dx2 - 2dy/dx + 2y = 0

Hence proved

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