What is the solution for y^{''}-7y^'+6y=3e^t ?

The solution for y^{''}-7y^'+6y=3e^t is y=c_{1}e^{6t}+c_{2}e^t-(3e^tt)/5

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y^{''}-7y^'+6y=3e^t

y^{^{''}} - 7 y^{^{'}} + 6 y = 3 e^{t}

y = c_{1} e^{6 t} + c_{2} e^{t} - \frac{3 e ^{t} t}{5}

Solution steps

y^{''} (t) - 7 y^{'} (t) + 6 y = 3 e^{t}

Solve linear ODE:

y = c_{1} e^{6 t} + c_{2} e^{t} - \frac{3 e ^{t} t}{5}

y = c_{1} e^{6 t} + c_{2} e^{t} - \frac{3 e ^{t} t}{5}

y^{^{''}} + 4 y = t e^{3 t} + 3 sin (4 t)

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

y^{^{''}} + 4 y^{^{'}} + 4 y = x^{2} - 2 x

y^{^{''}} + 25 y = 11 sec^{2} (5 t)

y^{^{''}} - 2 y^{^{'}} + 5 y = 3 e^{x} sin (x) + 24 x + 4

What is the solution for y^{''}-7y^'+6y=3e^t ?
The solution for y^{''}-7y^'+6y=3e^t is y=c_{1}e^{6t}+c_{2}e^t-(3e^tt)/5