The solution to the ordinary differential equation d2ydx2-dydx-6y-0 is

Given DE is d^2ydx^2+dydx 6y=0 Auxiliary equation is m^2+m 6=0 ⇒ (m+3)(m 2)=0 ⇒ m= 3,2 General solution is y=C_1e^ 3x+C_2e^2x ...

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Homogeneous Linear Differential Equations (General Form of LDE)

The solution ...

Question

The solution to the ordinary differential equation $\frac{d^{2} y}{d x^{2}} + \frac{d y}{d x} - 6 y = 0$ is

y = C_{1} e^{3 x} + C_{2} e^{- 2 x}

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y = C_{1} e^{3 x} + C_{2} e^{2 x}

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y = C_{1} e^{- 3 x} + C_{2} e^{2 x}

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y = C_{1} e^{- 3 x} + C_{2} e^{- 2 x}

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

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

y = c_{1} e^{- x} + c_{2} e^{- 3 x}

\frac{d^{2} y}{d x^{2}} + p \frac{d y}{d x} + (q + 1) y = 0

\frac{d^{2} y}{d x^{2}} - 5 \frac{d y}{d x} + 6 y = 0

$y = 4 s i n 3 x$ is a solution of the differential equation

[AI CBSE 1986]

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

\frac{d y}{d x} = 1 a t x = 0

\frac{d y}{d x} = 1 a t x = 1

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