What is the solution for (d^2y)/(dx^2)+(dy)/(dx)+1/4 y=0 ?

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

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(d^2y)/(dx^2)+(dy)/(dx)+1/4 y=0

\frac{d ^{2} y}{d x ^{2}} + \frac{d y}{d x} + \frac{1}{4} y = 0

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

Solution steps

\frac{d ^{2} y}{d x ^{2}} + \frac{d y}{d x} + \frac{1}{4} y = 0

Solve linear ODE:

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

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

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