What is the solution for (d^2y)/(dt^2)-12(dy)/(dt)+36y=7+4t ?

The solution for (d^2y)/(dt^2)-12(dy)/(dt)+36y=7+4t is y=c_{1}e^{6t}+c_{2}te^{6t}+t/9+25/108

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(d^2y)/(dt^2)-12(dy)/(dt)+36y=7+4t

\frac{d ^{2} y}{d t ^{2}} - 12 \frac{d y}{d t} + 36 y = 7 + 4 t

y = c_{1} e^{6 t} + c_{2} t e^{6 t} + \frac{t}{9} + \frac{25}{108}

Solution steps

\frac{d ^{2} y}{d t ^{2}} - 12 \frac{d y}{d t} + 36 y = 7 + 4 t

Solve linear ODE:

y = c_{1} e^{6 t} + c_{2} t e^{6 t} + \frac{t}{9} + \frac{25}{108}

y = c_{1} e^{6 t} + c_{2} t e^{6 t} + \frac{t}{9} + \frac{25}{108}

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

y^{^{''}} - 2 y^{^{'}} + 2 y = e^{(2 x)} \cdot sin (x)

y^{^{''}} - 15 y^{^{'}} + 54 y = e^{a x}

y^{^{'''}} + 9 y^{^{''}} + y^{^{'}} + 9 y = 16 e^{x} - 9

y^{^{''}} + 8 y^{^{'}} + 32 y = 2 e^{2 x}

What is the solution for (d^2y)/(dt^2)-12(dy)/(dt)+36y=7+4t ?
The solution for (d^2y)/(dt^2)-12(dy)/(dt)+36y=7+4t is y=c_{1}e^{6t}+c_{2}te^{6t}+t/9+25/108