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

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