Which of the following differential equations has y=c1ex+c2e−xas the general solution?(A) dx2d2y+y=0 (B) dx2d2y−y=0 (C) dx2d2y+1=0 (D) dx2d2y−1=0

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Which of the following differential equations has {y}={c}_{{1}

Question

Which of the following differential equations has $y = c_{1} e^{x} + c_{2} e^{- x}$ as the general solution?(A) $\frac{d ^{2} y}{d x ^{2}} + y = 0$ (B) $\frac{d ^{2} y}{d x ^{2}} - y = 0$ (C) $\frac{d ^{2} y}{d x ^{2}} + 1 = 0$ (D) $\frac{d ^{2} y}{d x ^{2}} - 1 = 0$

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Which of the following differential equations has

y = c_{1} e^{x} + c_{2} e^{- x}

as the general solution?(A)

\frac{d ^{2} y}{d x ^{2}} + y = 0

(B)

\frac{d ^{2} y}{d x ^{2}} - y = 0

(C)

\frac{d ^{2} y}{d x ^{2}} + 1 = 0

(D)

\frac{d ^{2} y}{d x ^{2}} - 1 = 0

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12 mins ago

Solution:

y = c_{1} e^{x} + c_{2} e^{- x}

differentiate with respect to x

y^{'} = c_{1} e^{x} - c_{2} e^{- x}

differentiate with respect to x

y^{''} = c_{1} e^{x} + c_{2} e^{- x}

y^{''} = y

y^{''} - y = 0

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Question Text	Which of the following differential equations has $y = c_{1} e^{x} + c_{2} e^{- x}$ as the general solution?(A) $\frac{d ^{2} y}{d x ^{2}} + y = 0$ (B) $\frac{d ^{2} y}{d x ^{2}} - y = 0$ (C) $\frac{d ^{2} y}{d x ^{2}} + 1 = 0$ (D) $\frac{d ^{2} y}{d x ^{2}} - 1 = 0$
Answer Type	Text solution:1
Upvotes	150