What is the solution for 3x^{''}-30x^'+75x=2t+1 ?

The solution for 3x^{''}-30x^'+75x=2t+1 is x=c_{1}e^{5t}+c_{2}te^{5t}+(2t)/(75)+3/125

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3x^{''}-30x^'+75x=2t+1

3 x^{^{''}} - 30 x^{^{'}} + 75 x = 2 t + 1

x = c_{1} e^{5 t} + c_{2} t e^{5 t} + \frac{2 t}{75} + \frac{3}{125}

Solution steps

3 x^{''} (t) - 30 x^{'} (t) + 75 x = 2 t + 1

Solve linear ODE:

x = c_{1} e^{5 t} + c_{2} t e^{5 t} + \frac{2 t}{75} + \frac{3}{125}

x = c_{1} e^{5 t} + c_{2} t e^{5 t} + \frac{2 t}{75} + \frac{3}{125}

y^{^{''}} - 6 y^{^{'}} + 5 y = 5 x^{2} + 3 x - 16 - 9 e^{2 x}

y^{^{''}} - 9 y = (x^{2} - 6) sin (3 x)

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

y^{^{''}} + y^{^{'}} - 6 y = 12 e^{3 t} + 12 e^{- 2 t}

y^{^{''}} + 3 y^{^{'}} = 2 x^{4}

What is the solution for 3x^{''}-30x^'+75x=2t+1 ?
The solution for 3x^{''}-30x^'+75x=2t+1 is x=c_{1}e^{5t}+c_{2}te^{5t}+(2t)/(75)+3/125