What is the solution for 4(d^2y)/(dx^2)-5y=0 ?

The solution for 4(d^2y)/(dx^2)-5y=0 is y=c_{1}e^{(sqrt(5)x)/2}+c_{2}e^{-(sqrt(5)x)/2}

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4(d^2y)/(dx^2)-5y=0

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

y = c_{1} e^{\frac{5 x}{2}} + c_{2} e^{- \frac{5 x}{2}}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{\frac{5 x}{2}} + c_{2} e^{- \frac{5 x}{2}}

y = c_{1} e^{\frac{5 x}{2}} + c_{2} e^{- \frac{5 x}{2}}

x \to 4 lim (\frac{sin ( x )}{x})

\frac{d y}{d x}, y e^{y} \cdot \frac{x - 1}{x + 1} = \frac{x ^{3}}{3} - x

\int_{0}^{8} x d x

\frac{\partial}{\partial x} (x y arcsin (yz))

y^{^{''}} - y^{^{'}} = \frac{1}{e ^{x} + e ^{- x}}

What is the solution for 4(d^2y)/(dx^2)-5y=0 ?
The solution for 4(d^2y)/(dx^2)-5y=0 is y=c_{1}e^{(sqrt(5)x)/2}+c_{2}e^{-(sqrt(5)x)/2}