What is the solution for (d^2y)/(dx^2)-5(dy)/(dx)+4y=0 ?

The solution for (d^2y)/(dx^2)-5(dy)/(dx)+4y=0 is y=c_{1}e^{4x}+c_{2}e^x

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(d^2y)/(dx^2)-5(dy)/(dx)+4y=0

\frac{d ^{2} y}{d x ^{2}} - 5 \frac{d y}{d x} + 4 y = 0

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

Solution steps

\frac{d ^{2} y}{d x ^{2}} - 5 \frac{d y}{d x} + 4 y = 0

Solve linear ODE:

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

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

y^{^{'''}} + 7 y^{^{''}} + 15 y^{^{'}} + 9 y = 0

4 y^{^{''}} + 3 y^{^{'}} = 0

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

\frac{d ^{2} y}{d x ^{2}} - 5 y = 0, y (0) = - 2, y (2) = 10

y^{^{''}} - 5 y^{^{'}} + 6 y = 0, y (0) = 0, y^{^{'}} (0) = 1

What is the solution for (d^2y)/(dx^2)-5(dy)/(dx)+4y=0 ?
The solution for (d^2y)/(dx^2)-5(dy)/(dx)+4y=0 is y=c_{1}e^{4x}+c_{2}e^x