What is the solution for (d^2y)/(dx^2)-6(dy)/(dx)+9y=54+18 ?

The solution for (d^2y)/(dx^2)-6(dy)/(dx)+9y=54+18 is y=c_{1}e^{3x}+c_{2}xe^{3x}+8

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(d^2y)/(dx^2)-6(dy)/(dx)+9y=54+18

\frac{d ^{2} y}{d x ^{2}} - 6 \frac{d y}{d x} + 9 y = 54 + 18

y = c_{1} e^{3 x} + c_{2} x e^{3 x} + 8

Solution steps

\frac{d ^{2} y}{d x ^{2}} - 6 \frac{d y}{d x} + 9 y = 54 + 18

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} x e^{3 x} + 8

y = c_{1} e^{3 x} + c_{2} x e^{3 x} + 8

d, d (x) = e^{2 x^{3} + 4}

x^{^{''}} + 4 x = sin (3 t)

(D^{2} - 4 D + 3) y = 9 x^{2} - 36 x + 37

y^{^{''}} + 4 y = x^{2} e^{- x}, y (0) = 0, y^{^{'}} (0) = 1

y^{^{''}} - 2 y^{^{'}} - 3 y = 6, y (0) = 9, y^{^{'}} (0) = 27

What is the solution for (d^2y)/(dx^2)-6(dy)/(dx)+9y=54+18 ?
The solution for (d^2y)/(dx^2)-6(dy)/(dx)+9y=54+18 is y=c_{1}e^{3x}+c_{2}xe^{3x}+8