What is the solution for 16y^{''}-8y^'+y=33-16x+x^2 ?

The solution for 16y^{''}-8y^'+y=33-16x+x^2 is y=c_{1}e^{x/4}+c_{2}e^{x/4}x+x^2+1

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16y^{''}-8y^'+y=33-16x+x^2

16 y^{^{''}} - 8 y^{^{'}} + y = 33 - 16 x + x^{2}

y = c_{1} e^{\frac{x}{4}} + c_{2} e^{\frac{x}{4}} x + x^{2} + 1

Solution steps

16 y^{''} (x) - 8 y^{'} (x) + y = 33 - 16 x + x^{2}

Solve linear ODE:

y = c_{1} e^{\frac{x}{4}} + c_{2} e^{\frac{x}{4}} x + x^{2} + 1

y = c_{1} e^{\frac{x}{4}} + c_{2} e^{\frac{x}{4}} x + x^{2} + 1

y^{^{''}} - 8 y^{^{'}} + 7 y = 4 e^{3} x

y^{^{''}} - 9 y^{^{'}} = \frac{9 x}{e ^{3 x}}

y^{^{''}} - 4 y^{^{'}} = 13 e^{12 x}

y^{^{''}} + y^{^{'}} - 2 y = sin (t)

y^{^{'''}} + 324 y^{^{'}} = tan (18 x)

What is the solution for 16y^{''}-8y^'+y=33-16x+x^2 ?
The solution for 16y^{''}-8y^'+y=33-16x+x^2 is y=c_{1}e^{x/4}+c_{2}e^{x/4}x+x^2+1