What is the solution for y^{''}-7y^'=(x-1)^2 ?

The solution for y^{''}-7y^'=(x-1)^2 is y=c_{1}e^{7x}+c_{2}-(x^3)/(21)+(6x^2)/(49)-(37x)/(343)

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y^{''}-7y^'=(x-1)^2

y^{^{''}} - 7 y^{^{'}} = (x - 1)^{2}

y = c_{1} e^{7 x} + c_{2} - \frac{x ^{3}}{21} + \frac{6 x ^{2}}{49} - \frac{37 x}{343}

Solution steps

y^{''} (x) - 7 y^{'} (x) = (x - 1)^{2}

Solve linear ODE:

y = c_{1} e^{7 x} + c_{2} - \frac{x ^{3}}{21} + \frac{6 x ^{2}}{49} - \frac{37 x}{343}

y = c_{1} e^{7 x} + c_{2} - \frac{x ^{3}}{21} + \frac{6 x ^{2}}{49} - \frac{37 x}{343}

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

y^{^{''}} + y = 8 cos (2 x) - 4 sin (x)

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

y^{^{''}} - y = e^{2 x}, y (0) = 1, y^{^{'}} (0) = 0

4 y^{^{''}} + y = cos (t)

What is the solution for y^{''}-7y^'=(x-1)^2 ?
The solution for y^{''}-7y^'=(x-1)^2 is y=c_{1}e^{7x}+c_{2}-(x^3)/(21)+(6x^2)/(49)-(37x)/(343)