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

The solution for y^{''}-4y^'=x-2 is y=c_{1}e^{4x}+c_{2}-(x^2)/8+(7x)/(16)

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

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

y = c_{1} e^{4 x} + c_{2} - \frac{x ^{2}}{8} + \frac{7 x}{16}

Solution steps

y^{''} (x) - 4 y^{'} (x) = x - 2

Solve linear ODE:

y = c_{1} e^{4 x} + c_{2} - \frac{x ^{2}}{8} + \frac{7 x}{16}

y = c_{1} e^{4 x} + c_{2} - \frac{x ^{2}}{8} + \frac{7 x}{16}

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What is the solution for y^{''}-4y^'=x-2 ?
The solution for y^{''}-4y^'=x-2 is y=c_{1}e^{4x}+c_{2}-(x^2)/8+(7x)/(16)