What is the solution for y^{''}-9y=e^{3x},y(0)=3,y^'(0)=10 ?

The solution for y^{''}-9y=e^{3x},y(0)=3,y^'(0)=10 is y=(3+5/36)e^{3x}-5/36 e^{-3x}+(e^{3x}x)/6

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y^{''}-9y=e^{3x},y(0)=3,y^'(0)=10

y^{^{''}} - 9 y = e^{3 x}, y (0) = 3, y^{^{'}} (0) = 10

y = (3 + \frac{5}{36}) e^{3 x} - \frac{5}{36} e^{- 3 x} + \frac{e ^{3 x} x}{6}

Solution steps

y^{''} (x) - 9 y = e^{3 x}

Solve linear ODE:

y = (3 + \frac{5}{36}) e^{3 x} - \frac{5}{36} e^{- 3 x} + \frac{e ^{3 x} x}{6}

y = (3 + \frac{5}{36}) e^{3 x} - \frac{5}{36} e^{- 3 x} + \frac{e ^{3 x} x}{6}

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

\frac{x ^{^{''}}}{2} + 10 x^{^{'}} + 100 x = 150

y^{^{''}} + a y^{^{'}} + b y = t + e^{3 t}

\frac{d ^{2} y}{d t ^{2}} - 3 \frac{d y}{d t} - 40 y = 5 + 4 t

y^{^{''}} + 4 x^{2} + 4 y = 6

What is the solution for y^{''}-9y=e^{3x},y(0)=3,y^'(0)=10 ?
The solution for y^{''}-9y=e^{3x},y(0)=3,y^'(0)=10 is y=(3+5/36)e^{3x}-5/36 e^{-3x}+(e^{3x}x)/6