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

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

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

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

y = c_{1} + c_{2} e^{- \frac{x}{4}}

Solution steps

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

Solve linear ODE:

y = c_{1} + c_{2} e^{- \frac{x}{4}}

y = c_{1} + c_{2} e^{- \frac{x}{4}}

y^{^{'''}} + 2 y^{^{''}} - 11 y^{^{'}} - 52 y = 0

\frac{d ^{2} f}{d x ^{2}} + 64 f (x) = 0

5 y^{^{''}} - 7 y^{^{'}} + 2 y = 0, y (0) = 1, y^{^{'}} (0) = - 0.8 y

(D^{3} - D^{2} - 8 D + 12) y = 0

2 y^{^{''}} - 5 y^{^{'}} - 7 y = 0, y^{^{'}} (0) = 3, y (0) = 4

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