What is the solution for (d^2-6d+9)y=2e^3x ?

The solution for (d^2-6d+9)y=2e^3x is y=c_{1}e^{3x}+c_{2}xe^{3x}+(2e^3x)/9+(4e^3)/(27)

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(d^2-6d+9)y=2e^3x

(d^{2} - 6 d + 9) y = 2 e^{3} x

y = c_{1} e^{3 x} + c_{2} x e^{3 x} + \frac{2 e ^{3} x}{9} + \frac{4 e ^{3}}{27}

Solution steps

(d^{2} - 6 d + 9) y = 2 e^{3} x

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} x e^{3 x} + \frac{2 e ^{3} x}{9} + \frac{4 e ^{3}}{27}

y = c_{1} e^{3 x} + c_{2} x e^{3 x} + \frac{2 e ^{3} x}{9} + \frac{4 e ^{3}}{27}

y^{^{''}} + 3 y^{^{'}} + 2 y = (e^{e})^{x}

y^{^{''}} - 5 y^{^{'}} + 6 y = 2 e^{x}

(d^{2} - 1) \cdot y = x \cdot sin (x) + x^{2} \cdot e^{x}

d, d (x) = \frac{1}{36 ( x - 60 ) ^{2} - 100}

(d^{2} + 2 d + 1) \cdot y = x \cdot e^{- x} \cdot cos (x)

What is the solution for (d^2-6d+9)y=2e^3x ?
The solution for (d^2-6d+9)y=2e^3x is y=c_{1}e^{3x}+c_{2}xe^{3x}+(2e^3x)/9+(4e^3)/(27)