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

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

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4y^{''}-4y^'+y=16e^{x/2}

4 y^{^{''}} - 4 y^{^{'}} + y = 16 e^{\frac{x}{2}}

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

Solution steps

4 y^{''} (x) - 4 y^{'} (x) + y = 16 e^{\frac{x}{2}}

Solve linear ODE:

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

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

y^{^{''}} - y^{^{'}} = e^{x} sin (x)

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

y^{^{'''}} - y^{^{''}} - 4 y^{^{'}} + 4 y = 20 e^{3 t}

y^{^{''}} - 8 y^{^{'}} + 17 y = 10 e^{4 x} sec (x)

y^{^{''}} - 4 y = 12

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