What is the solution for y^{''}-9y^'+14y=30t-34 ?

The solution for y^{''}-9y^'+14y=30t-34 is y=c_{1}e^{7t}+c_{2}e^{2t}+(15t)/7-103/98

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y^{''}-9y^'+14y=30t-34

y^{^{''}} - 9 y^{^{'}} + 14 y = 30 t - 34

y = c_{1} e^{7 t} + c_{2} e^{2 t} + \frac{15 t}{7} - \frac{103}{98}

Solution steps

y^{''} (t) - 9 y^{'} (t) + 14 y = 30 t - 34

Solve linear ODE:

y = c_{1} e^{7 t} + c_{2} e^{2 t} + \frac{15 t}{7} - \frac{103}{98}

y = c_{1} e^{7 t} + c_{2} e^{2 t} + \frac{15 t}{7} - \frac{103}{98}

y^{^{''}} + y = 6 sin (2 t), y (0) = 3, y^{^{'}} (0) = 1

\frac{d ^{2} y}{d x ^{2}} + 4 y = x

y^{^{''}} + 6 y^{^{'}} + 8 y = e sin (x)

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

(\frac{d ^{2} + 120 d + 1}{10}) y = 12

What is the solution for y^{''}-9y^'+14y=30t-34 ?
The solution for y^{''}-9y^'+14y=30t-34 is y=c_{1}e^{7t}+c_{2}e^{2t}+(15t)/7-103/98