What is the solution for y^{''}-6y^'+5y=x,y^1(0)=e^x ?

The solution for y^{''}-6y^'+5y=x,y^1(0)=e^x is y=c_{1}e^{5x}+c_{2}e^x+x/5+6/25

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y^{''}-6y^'+5y=x,y^1(0)=e^x

y^{^{''}} - 6 y^{^{'}} + 5 y = x, y^{1} (0) = e^{x}

y = c_{1} e^{5 x} + c_{2} e^{x} + \frac{x}{5} + \frac{6}{25}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{5 x} + c_{2} e^{x} + \frac{x}{5} + \frac{6}{25}

y = c_{1} e^{5 x} + c_{2} e^{x} + \frac{x}{5} + \frac{6}{25}

What is the solution for y^{''}-6y^'+5y=x,y^1(0)=e^x ?
The solution for y^{''}-6y^'+5y=x,y^1(0)=e^x is y=c_{1}e^{5x}+c_{2}e^x+x/5+6/25