What is the solution for y^{''}-14y^'+49y=49x+4 ?

The solution for y^{''}-14y^'+49y=49x+4 is y=c_{1}e^{7x}+c_{2}xe^{7x}+x+18/49

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y^{''}-14y^'+49y=49x+4

y^{^{''}} - 14 y^{^{'}} + 49 y = 49 x + 4

y = c_{1} e^{7 x} + c_{2} x e^{7 x} + x + \frac{18}{49}

Solution steps

y^{''} (x) - 14 y^{'} (x) + 49 y = 49 x + 4

Solve linear ODE:

y = c_{1} e^{7 x} + c_{2} x e^{7 x} + x + \frac{18}{49}

y = c_{1} e^{7 x} + c_{2} x e^{7 x} + x + \frac{18}{49}

y^{^{''}} + 3 y^{^{'}} = 7

y^{^{''}} - 6 y^{^{'}} + 25 y = 64 e^{- x}

y^{^{''}} + 9 y = 5 e^{x} - 162 x^{2}

y^{^{''}} + 3 y^{^{'}} + 2 y = (1 + e^{x})^{- 1}

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

What is the solution for y^{''}-14y^'+49y=49x+4 ?
The solution for y^{''}-14y^'+49y=49x+4 is y=c_{1}e^{7x}+c_{2}xe^{7x}+x+18/49