What is the solution for y^{'''}-5y^{''}+6y^'=3+7x ?

The solution for y^{'''}-5y^{''}+6y^'=3+7x is y=c_{1}+c_{2}e^{2x}+c_{3}e^{3x}+(7x^2)/(12)+(53x)/(36)

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y^{'''}-5y^{''}+6y^'=3+7x

y^{^{'''}} - 5 y^{^{''}} + 6 y^{^{'}} = 3 + 7 x

y = c_{1} + c_{2} e^{2 x} + c_{3} e^{3 x} + \frac{7 x ^{2}}{12} + \frac{53 x}{36}

Solution steps

y^{'''} (x) - 5 y^{''} (x) + 6 y^{'} (x) = 3 + 7 x

Solve linear ODE:

y = c_{1} + c_{2} e^{2 x} + c_{3} e^{3 x} + \frac{7 x ^{2}}{12} + \frac{53 x}{36}

y = c_{1} + c_{2} e^{2 x} + c_{3} e^{3 x} + \frac{7 x ^{2}}{12} + \frac{53 x}{36}

What is the solution for y^{'''}-5y^{''}+6y^'=3+7x ?
The solution for y^{'''}-5y^{''}+6y^'=3+7x is y=c_{1}+c_{2}e^{2x}+c_{3}e^{3x}+(7x^2)/(12)+(53x)/(36)