What is the solution for (d^2y)/(dx^2)-6(dy)/(dx)+3y=0 ?

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

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(d^2y)/(dx^2)-6(dy)/(dx)+3y=0

\frac{d ^{2} y}{d x ^{2}} - 6 \frac{d y}{d x} + 3 y = 0

y = c_{1} e^{(3 + 6) x} + c_{2} e^{(3 - 6) x}

Solution steps

\frac{d ^{2} y}{d x ^{2}} - 6 \frac{d y}{d x} + 3 y = 0

Solve linear ODE:

y = c_{1} e^{(3 + 6) x} + c_{2} e^{(3 - 6) x}

y = c_{1} e^{(3 + 6) x} + c_{2} e^{(3 - 6) x}

\frac{d ^{4} y}{d x ^{4}} + 6 \frac{d ^{2} y}{d x ^{2}} + 8 y = 0

y^{^{''}} + 9 y^{^{'}} - 20 y = 0

y^{^{''}} - 20 y^{^{'}} + 64 y = 0

f^{^{''}} (t) - c f (t) = 0

y^{^{'''}} + 8 y^{^{''}} + 25 y^{^{'}} = 0

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