What is the solution for y^{''}-6y^'+5y=-1+5x ?

The solution for y^{''}-6y^'+5y=-1+5x is y=c_{1}e^{5x}+c_{2}e^x+x+1

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y^{''}-6y^'+5y=-1+5x

y^{^{''}} - 6 y^{^{'}} + 5 y = - 1 + 5 x

y = c_{1} e^{5 x} + c_{2} e^{x} + x + 1

Solution steps

y^{''} (x) - 6 y^{'} (x) + 5 y = - 1 + 5 x

Solve linear ODE:

y = c_{1} e^{5 x} + c_{2} e^{x} + x + 1

y = c_{1} e^{5 x} + c_{2} e^{x} + x + 1

y^{^{''}} - 6 y^{^{'}} + 9 y = 8 e^{3 x}

y^{^{''}} + 4 y = 8 tan^{2} (2 x)

y^{^{''}} + 4 y^{^{'}} = 8

y^{^{'''}} - 4 y^{^{''}} + 5 y^{^{'}} = 40 t - 7 - 6 e^{2 t}

y^{^{''}} + 3 y^{^{'}} = - e^{2 x} + e^{3 x}

What is the solution for y^{''}-6y^'+5y=-1+5x ?
The solution for y^{''}-6y^'+5y=-1+5x is y=c_{1}e^{5x}+c_{2}e^x+x+1