What is the solution for 4(d^2y)/(dx^2)-4(dy)/(dx)-3y=0 ?

The solution for 4(d^2y)/(dx^2)-4(dy)/(dx)-3y=0 is y=c_{1}e^{(3x)/2}+c_{2}e^{-x/2}

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4(d^2y)/(dx^2)-4(dy)/(dx)-3y=0

4 \frac{d ^{2} y}{d x ^{2}} - 4 \frac{d y}{d x} - 3 y = 0

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

Solution steps

4 \frac{d ^{2} y}{d x ^{2}} - 4 \frac{d y}{d x} - 3 y = 0

Solve linear ODE:

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

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

y^{^{''''}} + 2 y^{^{'''}} + 37 y^{^{''}} + 72 y^{^{'}} + 36 y = 0

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

y^{^{'''}} + 3.2 y^{^{''}} + 4.81 y^{^{'}} = 0

3 y^{^{''}} + 27 y^{^{'}} + 42 y = 0

y^{^{''}} - 16 y = 0, y (0) = 4

What is the solution for 4(d^2y)/(dx^2)-4(dy)/(dx)-3y=0 ?
The solution for 4(d^2y)/(dx^2)-4(dy)/(dx)-3y=0 is y=c_{1}e^{(3x)/2}+c_{2}e^{-x/2}