What is the solution for y^{''}-6y^'+9y=2,y^'(0)=6 ?

The solution for y^{''}-6y^'+9y=2,y^'(0)=6 is y=(e^{3t}(6-c_{2}))/3+c_{2}e^{3t}t+2/9

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

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

y = \frac{e ^{3 t} ( 6 - c _{2} )}{3} + c_{2} e^{3 t} t + \frac{2}{9}

Solution steps

y^{''} (t) - 6 y^{'} (t) + 9 y = 2

Solve linear ODE:

y = \frac{e ^{3 t} ( 6 - c _{2} )}{3} + c_{2} e^{3 t} t + \frac{2}{9}

y = \frac{e ^{3 t} ( 6 - c _{2} )}{3} + c_{2} e^{3 t} t + \frac{2}{9}

y^{^{''}} - 2 y^{^{'}} - 15 y = - 37 t + 30 t^{2}

y^{^{''}} - y^{^{'}} - 6 y = 4 cos (3 x)

y^{^{'''}} + 3 y^{^{''}} - 4 y^{^{'}} - 12 y = 4 cos (x)

y^{^{'''}} - a y^{^{'}} = 1 + cosh (a x)

y^{^{''}} + 5 y^{^{'}} + 8 y = 24 + 23 x + 12 x^{2}

What is the solution for y^{''}-6y^'+9y=2,y^'(0)=6 ?
The solution for y^{''}-6y^'+9y=2,y^'(0)=6 is y=(e^{3t}(6-c_{2}))/3+c_{2}e^{3t}t+2/9