What is the solution for y^{''}-3y^'+2y=e^{3t} ?

The solution for y^{''}-3y^'+2y=e^{3t} is y=c_{1}e^{2t}+c_{2}e^t+1/2 e^{3t}

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y^{''}-3y^'+2y=e^{3t}

y^{^{''}} - 3 y^{^{'}} + 2 y = e^{3 t}

y = c_{1} e^{2 t} + c_{2} e^{t} + \frac{1}{2} e^{3 t}

Solution steps

y^{''} (t) - 3 y^{'} (t) + 2 y = e^{3 t}

Solve linear ODE:

y = c_{1} e^{2 t} + c_{2} e^{t} + \frac{1}{2} e^{3 t}

y = c_{1} e^{2 t} + c_{2} e^{t} + \frac{1}{2} e^{3 t}

\frac{\partial}{\partial x} (x^{s i n (x)})

6 \cdot (\frac{d y}{d x}) = y^{2}, y (0) = 4

y = x^{3} - 2 x + 2, (3, 23)

\frac{d y}{d x} = \frac{( 3 y ^{2} )}{x}

y^{^{'}} = \frac{( x ^{2} y - y )}{y + 1}

What is the solution for y^{''}-3y^'+2y=e^{3t} ?
The solution for y^{''}-3y^'+2y=e^{3t} is y=c_{1}e^{2t}+c_{2}e^t+1/2 e^{3t}