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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} + 4 y = t^{2} + 4 e t, y (0) = 0, y^{^{'}} (0) = 3

y^{^{''}} + 9 y = 18 (sec (3 x))^{3}

y^{^{''}} - 3 y^{^{'}} - 4 y = 6

3 y^{^{''}} + 192.08 y = 48.02 cos (8 t)

y^{^{''}} - 2 y^{^{'}} - 24 y = 16 - (x + 2) e^{4 x}

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