What is the solution for y^{''}-3y^'+2y=7x+28 ?

The solution for y^{''}-3y^'+2y=7x+28 is y=c_{1}e^{2x}+c_{2}e^x+(7x)/2+77/4

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y^{''}-3y^'+2y=7x+28

y^{^{''}} - 3 y^{^{'}} + 2 y = 7 x + 28

y = c_{1} e^{2 x} + c_{2} e^{x} + \frac{7 x}{2} + \frac{77}{4}

Solution steps

y^{''} (x) - 3 y^{'} (x) + 2 y = 7 x + 28

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{x} + \frac{7 x}{2} + \frac{77}{4}

y = c_{1} e^{2 x} + c_{2} e^{x} + \frac{7 x}{2} + \frac{77}{4}

4 y^{^{''}} - y = e^{x}

y^{^{''}} - 2 y^{^{'}} + 1 = x^{2}

y^{^{''}} - 4 y^{^{'}} + 3 y = 3 t e^{t}, y (0) = 1, y^{^{'}} (0) = - 5

y^{^{''}} - 3 y^{^{'}} - 4 y = 8 e^{x} cos (2 x)

y^{^{''}} + 6 y^{^{'}} + 5 y = - 1020 sin (3 t)

What is the solution for y^{''}-3y^'+2y=7x+28 ?
The solution for y^{''}-3y^'+2y=7x+28 is y=c_{1}e^{2x}+c_{2}e^x+(7x)/2+77/4