What is the solution for y^{''}-10y^'+24y=90e^t ?

The solution for y^{''}-10y^'+24y=90e^t is y=c_{1}e^{6t}+c_{2}e^{4t}+6e^t

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y^{''}-10y^'+24y=90e^t

y^{^{''}} - 10 y^{^{'}} + 24 y = 90 e^{t}

y = c_{1} e^{6 t} + c_{2} e^{4 t} + 6 e^{t}

Solution steps

y^{''} (t) - 10 y^{'} (t) + 24 y = 90 e^{t}

Solve linear ODE:

y = c_{1} e^{6 t} + c_{2} e^{4 t} + 6 e^{t}

y = c_{1} e^{6 t} + c_{2} e^{4 t} + 6 e^{t}

y^{^{''}} + 9 y^{^{'}} = 8 sin (t), y (0) = 1, y^{^{'}} (0) = 1

y^{^{''}} + 2 y^{^{'}} + 17 = 0, y (0) = 1, y^{^{'}} (0) = - 1

y^{^{''}} + 3 y = cos (3 x)

y^{^{''}} + 40 y^{^{'}} + 400 y = 100 sin (10 t)

y^{^{''}} + 7 y = x

What is the solution for y^{''}-10y^'+24y=90e^t ?
The solution for y^{''}-10y^'+24y=90e^t is y=c_{1}e^{6t}+c_{2}e^{4t}+6e^t