What is the solution for y^{''}-14y^'+49y=(x+1)e^x ?

The solution for y^{''}-14y^'+49y=(x+1)e^x is y=c_{1}e^{7x}+c_{2}xe^{7x}+(e^xx)/(36)+1/27 e^x

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y^{''}-14y^'+49y=(x+1)e^x

y^{^{''}} - 14 y^{^{'}} + 49 y = (x + 1) e^{x}

y = c_{1} e^{7 x} + c_{2} x e^{7 x} + \frac{e ^{x} x}{36} + \frac{1}{27} e^{x}

Solution steps

y^{''} (x) - 14 y^{'} (x) + 49 y = (x + 1) e^{x}

Solve linear ODE:

y = c_{1} e^{7 x} + c_{2} x e^{7 x} + \frac{e ^{x} x}{36} + \frac{1}{27} e^{x}

y = c_{1} e^{7 x} + c_{2} x e^{7 x} + \frac{e ^{x} x}{36} + \frac{1}{27} e^{x}

y^{^{''}} - 10 y^{^{'}} + 25 y = 4 e^{5 x}

y^{^{''}} + 10 y^{^{'}} + 25 y = 50 sin (5 x)

y^{^{''}} + 4 y^{^{'}} + 4 y = 2 x

y^{^{''}} + 6 y^{^{'}} + 34 y = 30 cos (2 t)

y^{^{''}} - 7 y^{^{'}} + 9 y = x e^{x}

What is the solution for y^{''}-14y^'+49y=(x+1)e^x ?
The solution for y^{''}-14y^'+49y=(x+1)e^x is y=c_{1}e^{7x}+c_{2}xe^{7x}+(e^xx)/(36)+1/27 e^x