What is the solution for (d^2y)/(dx^2)-11/2 (dy)/(dx)+6y=0 ?

The solution for (d^2y)/(dx^2)-11/2 (dy)/(dx)+6y=0 is y=c_{1}e^{4x}+c_{2}e^{(3x)/2}

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(d^2y)/(dx^2)-11/2 (dy)/(dx)+6y=0

\frac{d ^{2} y}{d x ^{2}} - \frac{11}{2} \frac{d y}{d x} + 6 y = 0

y = c_{1} e^{4 x} + c_{2} e^{\frac{3 x}{2}}

Solution steps

\frac{d ^{2} y}{d x ^{2}} - \frac{11}{2} \frac{d y}{d x} + 6 y = 0

Solve linear ODE:

y = c_{1} e^{4 x} + c_{2} e^{\frac{3 x}{2}}

y = c_{1} e^{4 x} + c_{2} e^{\frac{3 x}{2}}

y^{^{'''}} - 27 y = 0

(D^{2} - 6 D + 9) y = 0

4 y^{^{''}} + 4 y^{^{'}} + 512 y = 0, y (0) = 0, y^{^{'}} (0) = 7

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

y^{^{''}} + 10 y^{^{'}} + 16 y = 0, y (0) = 0, y^{^{'}} (0) = - 6

What is the solution for (d^2y)/(dx^2)-11/2 (dy)/(dx)+6y=0 ?
The solution for (d^2y)/(dx^2)-11/2 (dy)/(dx)+6y=0 is y=c_{1}e^{4x}+c_{2}e^{(3x)/2}