What is the solution for y^{''}-14y^'+49y=14x+3 ?

The solution for y^{''}-14y^'+49y=14x+3 is y=c_{1}e^{7x}+c_{2}xe^{7x}+(2x)/7+1/7

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y^{''}-14y^'+49y=14x+3

y^{^{''}} - 14 y^{^{'}} + 49 y = 14 x + 3

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

Solution steps

y^{''} (x) - 14 y^{'} (x) + 49 y = 14 x + 3

Solve linear ODE:

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

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

y^{^{'''}} + y^{^{''}} - y^{^{'}} - 1 = 2 (1 + e^{- x})

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

y^{^{''}} + 4 y = \frac{2}{sin ( 2 x )}

x^{^{''}} + 3 x^{^{'}} + 2 x = 5 cos (t) + sin (2 t)

3 x^{^{''}} + 53 x = 5 cos (4 t)

What is the solution for y^{''}-14y^'+49y=14x+3 ?
The solution for y^{''}-14y^'+49y=14x+3 is y=c_{1}e^{7x}+c_{2}xe^{7x}+(2x)/7+1/7