What is the solution for y^{''}-14y^'+49y=21x+2 ?

The solution for y^{''}-14y^'+49y=21x+2 is y=c_{1}e^{7x}+c_{2}xe^{7x}+(3x)/7+8/49

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y^{''}-14y^'+49y=21x+2

y^{^{''}} - 14 y^{^{'}} + 49 y = 21 x + 2

y = c_{1} e^{7 x} + c_{2} x e^{7 x} + \frac{3 x}{7} + \frac{8}{49}

Solution steps

y^{''} (x) - 14 y^{'} (x) + 49 y = 21 x + 2

Solve linear ODE:

y = c_{1} e^{7 x} + c_{2} x e^{7 x} + \frac{3 x}{7} + \frac{8}{49}

y = c_{1} e^{7 x} + c_{2} x e^{7 x} + \frac{3 x}{7} + \frac{8}{49}

y^{^{''}} + 4 y^{^{'}} + 5 y = - 15 x + 3 e^{- x}

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

y^{^{''}} - 4 y^{^{'}} - 5 y = 2 + e^{- t}

y^{^{''}} + 16 y = e^{- 4 t} + 3 sin (4 t)

\frac{d ^{2} y}{d x ^{2}} + y = 5 sin (4 x)

What is the solution for y^{''}-14y^'+49y=21x+2 ?
The solution for y^{''}-14y^'+49y=21x+2 is y=c_{1}e^{7x}+c_{2}xe^{7x}+(3x)/7+8/49