What is the solution for (d^2y)/(dx^2)-7(dy)/(dx)+6y=0 ?

The solution for (d^2y)/(dx^2)-7(dy)/(dx)+6y=0 is y=c_{1}e^{6x}+c_{2}e^x

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(d^2y)/(dx^2)-7(dy)/(dx)+6y=0

\frac{d ^{2} y}{d x ^{2}} - 7 \frac{d y}{d x} + 6 y = 0

y = c_{1} e^{6 x} + c_{2} e^{x}

Solution steps

\frac{d ^{2} y}{d x ^{2}} - 7 \frac{d y}{d x} + 6 y = 0

Solve linear ODE:

y = c_{1} e^{6 x} + c_{2} e^{x}

y = c_{1} e^{6 x} + c_{2} e^{x}

x^{^{''}} + 10 x^{^{'}} + 15 x = 0

y^{^{''}} + (3 - α) y^{^{'}} - 2 (α - 1) y = 0

2 y^{^{''}} + 5 y^{^{'}} - 3 y = 0, y (0) = 5, y^{^{''}} (0) = 13

y^{^{''}} + 2 y^{^{'}} + 2 y = 0, y (0) = 0, y^{^{'}} (0) = 0

\frac{d ^{2} y}{d x ^{2}} + \frac{d y}{d x} + 5 y = 0

What is the solution for (d^2y)/(dx^2)-7(dy)/(dx)+6y=0 ?
The solution for (d^2y)/(dx^2)-7(dy)/(dx)+6y=0 is y=c_{1}e^{6x}+c_{2}e^x