What is the solution for (dx)/(dt)=3x+e^{2t}-2e^{3t}+e^{4t} ?

The solution for (dx)/(dt)=3x+e^{2t}-2e^{3t}+e^{4t} is x=-e^{2t}-2e^{3t}t+e^{4t}+c_{1}e^{3t}

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(dx)/(dt)=3x+e^{2t}-2e^{3t}+e^{4t}

\frac{d x}{d t} = 3 x + e^{2 t} - 2 e^{3 t} + e^{4 t}

x = - e^{2 t} - 2 e^{3 t} t + e^{4 t} + c_{1} e^{3 t}

Solution steps

\frac{d x}{d t} = 3 x + e^{2 t} - 2 e^{3 t} + e^{4 t}

Solve linear ODE:

x = - e^{2 t} - 2 e^{3 t} t + e^{4 t} + c_{1} e^{3 t}

x = - e^{2 t} - 2 e^{3 t} t + e^{4 t} + c_{1} e^{3 t}

What is the solution for (dx)/(dt)=3x+e^{2t}-2e^{3t}+e^{4t} ?
The solution for (dx)/(dt)=3x+e^{2t}-2e^{3t}+e^{4t} is x=-e^{2t}-2e^{3t}t+e^{4t}+c_{1}e^{3t}