What is the solution for (d^2y)/(dx^2)(1)-(dy)/(dx)(5)+4y=0 ?

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

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(d^2y)/(dx^2)(1)-(dy)/(dx)(5)+4y=0

\frac{d ^{2} y}{d x ^{2}} (1) - \frac{d y}{d x} (5) + 4 y = 0

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

Solution steps

\frac{d ^{2} y}{d x ^{2}} (1) - \frac{d y}{d x} (5) + 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}

2 x^{^{''}} + 2 x^{^{'}} + 3 x = 0

y^{^{''}} + a y = 0, y^{^{'}} (0) = 0, y (1) = 0

3 y^{^{''}} + 2 y^{^{'}} + 4 y^{^{''}} + y = 0

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

y^{^{''}} = y^{^{'}} - 2 y

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