What is the solution for y^{''}-14y^'+49y=10e^{7x} ?

The solution for y^{''}-14y^'+49y=10e^{7x} is y=c_{1}e^{7x}+c_{2}xe^{7x}+5x^2e^{7x}

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y^{''}-14y^'+49y=10e^{7x}

y^{^{''}} - 14 y^{^{'}} + 49 y = 10 e^{7 x}

y = c_{1} e^{7 x} + c_{2} x e^{7 x} + 5 x^{2} e^{7 x}

Solution steps

y^{''} (x) - 14 y^{'} (x) + 49 y = 10 e^{7 x}

Solve linear ODE:

y = c_{1} e^{7 x} + c_{2} x e^{7 x} + 5 x^{2} e^{7 x}

y = c_{1} e^{7 x} + c_{2} x e^{7 x} + 5 x^{2} e^{7 x}

y^{^{''}} + y^{^{'}} - 12 y = sin (t), y (0) = 1, y^{^{'}} (0) = 1

y, (d^{2} + 5 d + 6) y = (d + 1) 6 t^{2}

y^{^{''}} - 6 y^{^{'}} + 10 y = 10 x^{2} + 8 x

y^{^{''}} + y^{^{'}} = 8 x^{2}

y^{^{''}} + y^{^{'}} - 6 y = e^{4 x}

What is the solution for y^{''}-14y^'+49y=10e^{7x} ?
The solution for y^{''}-14y^'+49y=10e^{7x} is y=c_{1}e^{7x}+c_{2}xe^{7x}+5x^2e^{7x}