What is the solution for D(D-3)y=3t+t/2 ?

The solution for D(D-3)y=3t+t/2 is y=c_{1}+c_{2}e^{3t}-(7t^2)/(12)-(7t)/(18)

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D(D-3)y=3t+t/2

D (D - 3) y = 3 t + \frac{t}{2}

y = c_{1} + c_{2} e^{3 t} - \frac{7 t ^{2}}{12} - \frac{7 t}{18}

Solution steps

D (D - 3) y = 3 t + \frac{t}{2}

Solve linear ODE:

y = c_{1} + c_{2} e^{3 t} - \frac{7 t ^{2}}{12} - \frac{7 t}{18}

y = c_{1} + c_{2} e^{3 t} - \frac{7 t ^{2}}{12} - \frac{7 t}{18}

8 y^{^{''}} - 6 y^{^{'}} + y = 6 cosh (x)

y^{^{''}} - 100 y = 15

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

y^{^{''}} - y^{^{'}} - 2 y = 2 sin (x)

y^{^{''}} + 16 y = 16 sin (4 x)

What is the solution for D(D-3)y=3t+t/2 ?
The solution for D(D-3)y=3t+t/2 is y=c_{1}+c_{2}e^{3t}-(7t^2)/(12)-(7t)/(18)