What is the solution for y^{''}-7y^'+12=x ?

The solution for y^{''}-7y^'+12=x is y=c_{1}e^{7x}+c_{2}-(x^2)/(14)+(83x)/(49)

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y^{''}-7y^'+12=x

y^{^{''}} - 7 y^{^{'}} + 12 = x

y = c_{1} e^{7 x} + c_{2} - \frac{x ^{2}}{14} + \frac{83 x}{49}

Solution steps

y^{''} (x) - 7 y^{'} (x) + 12 = x

Solve linear ODE:

y = c_{1} e^{7 x} + c_{2} - \frac{x ^{2}}{14} + \frac{83 x}{49}

y = c_{1} e^{7 x} + c_{2} - \frac{x ^{2}}{14} + \frac{83 x}{49}

What is the solution for y^{''}-7y^'+12=x ?
The solution for y^{''}-7y^'+12=x is y=c_{1}e^{7x}+c_{2}-(x^2)/(14)+(83x)/(49)