What is the solution for y^{''}-14*y^{''}+45*y^'=32e^x ?

The solution for y^{''}-14*y^{''}+45*y^'=32e^x is y=c_{1}+c_{2}e^{(45x)/(13)}+e^x

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y^{''}-14y^{''}+45y^'=32e^x

y^{^{''}} - 14 \cdot y^{^{''}} + 45 \cdot y^{^{'}} = 32 e^{x}

y = c_{1} + c_{2} e^{\frac{45 x}{13}} + e^{x}

Solution steps

y^{''} (x) - 14 \cdot y^{''} (x) + 45 \cdot y^{'} (x) = 32 e^{x}

Solve linear ODE:

y = c_{1} + c_{2} e^{\frac{45 x}{13}} + e^{x}

y = c_{1} + c_{2} e^{\frac{45 x}{13}} + e^{x}

y^{^{''}} - y^{^{'}} - 6 y = 4 t e^{3} t, y (0) = - 5, y^{^{'}} (0) = - 3

y^{^{''}} + y^{^{'}} - 2 y = - 4, y (0) = 2, y^{^{'}} (0) = 3

- y^{^{''}} + y^{^{'}} + 2 y = e^{t}

y^{^{''}} - 4 y^{^{'}} - 21 y = 800 e^{- t}

y^{^{''}} + 5 y^{^{'}} + 4 y = 13 t e^{4 t}

What is the solution for y^{''}-14*y^{''}+45*y^'=32e^x ?
The solution for y^{''}-14*y^{''}+45*y^'=32e^x is y=c_{1}+c_{2}e^{(45x)/(13)}+e^x