What is the solution for y^{'''}=3y^{''}+9*e^x+0*cos(x) ?

The solution for y^{'''}=3y^{''}+9*e^x+0*cos(x) is y=c_{1}e^{3x}+c_{2}+c_{3}x-9/2 e^x

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y^{'''}=3y^{''}+9e^x+0cos(x)

y^{^{'''}} = 3 y^{^{''}} + 9 \cdot e^{x} + 0 \cdot cos (x)

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

Solution steps

y^{'''} (x) = 3 y^{''} (x) + 9 \cdot e^{x} + 0 \cdot cos (x)

Solve linear ODE:

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

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

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

y^{^{'''}} - 7 y^{^{''}} + 14 y^{^{'}} - 8 y = ln (x)

y^{^{''}} + 5 y + 4 y = 5 e^{- 5 x}, y (0) = - 2, y^{^{'}} (0) = 2

y^{^{''}} + 5 y^{^{'}} + 4 y = 17 t e^{5 t}

y^{^{''}} - y = 9.5 cos (t)

What is the solution for y^{'''}=3y^{''}+9*e^x+0*cos(x) ?
The solution for y^{'''}=3y^{''}+9*e^x+0*cos(x) is y=c_{1}e^{3x}+c_{2}+c_{3}x-9/2 e^x