What is the solution for y^{'''}+49y^'=5x+6 ?

The solution for y^{'''}+49y^'=5x+6 is y=c_{1}+c_{2}cos(7x)+c_{3}sin(7x)+(5x^2)/(98)+(6x)/(49)

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y^{'''}+49y^'=5x+6

y^{^{'''}} + 49 y^{^{'}} = 5 x + 6

y = c_{1} + c_{2} cos (7 x) + c_{3} sin (7 x) + \frac{5 x ^{2}}{98} + \frac{6 x}{49}

Solution steps

y^{'''} (x) + 49 y^{'} (x) = 5 x + 6

Solve linear ODE:

y = c_{1} + c_{2} cos (7 x) + c_{3} sin (7 x) + \frac{5 x ^{2}}{98} + \frac{6 x}{49}

y = c_{1} + c_{2} cos (7 x) + c_{3} sin (7 x) + \frac{5 x ^{2}}{98} + \frac{6 x}{49}

y^{^{''}} - 6 y^{^{'}} + 9 y = x^{- 4} \cdot e^{3} x

3 y^{^{''}} + 4 y = 3 e^{3} x

y^{^{''}} - 2 y^{^{'}} + 2 y = e x, y (\frac{π}{2}) = 0, y (0) = 0

y^{^{''}} + y^{^{'}} - 6 y = 18

x^{^{''}} + 4 x^{^{'}} + 20 x = 4 cos (2 t)

What is the solution for y^{'''}+49y^'=5x+6 ?
The solution for y^{'''}+49y^'=5x+6 is y=c_{1}+c_{2}cos(7x)+c_{3}sin(7x)+(5x^2)/(98)+(6x)/(49)