What is the solution for 3y^'+7y=x^3-2x^2+1 ?

The solution for 3y^'+7y=x^3-2x^2+1 is y=(343x^3-1127x^2+966x-71}{2401}+(c_{1})/(e^{\frac{7x)/3)}

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3y^'+7y=x^3-2x^2+1

3 y^{^{'}} + 7 y = x^{3} - 2 x^{2} + 1

y = \frac{343 x ^{3} - 1127 x ^{2} + 966 x - 71}{2401} + \frac{c _{1}}{e ^{\frac{7 x}{3}}}

Solution steps

3 y^{'} (x) + 7 y = x^{3} - 2 x^{2} + 1

Solve linear ODE:

y = \frac{343 x ^{3} - 1127 x ^{2} + 966 x - 71}{2401} + \frac{c _{1}}{e ^{\frac{7 x}{3}}}

y = \frac{343 x ^{3} - 1127 x ^{2} + 966 x - 71}{2401} + \frac{c _{1}}{e ^{\frac{7 x}{3}}}

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

y^{^{'}} = y + e^{x}, y (0) = (x + c) e^{x}, y (0) = \frac{1}{2}

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

y^{^{'}} = 2 y + (x^{2}) + 5

(x - 1) y^{^{'}} + x y = sin (x)

What is the solution for 3y^'+7y=x^3-2x^2+1 ?
The solution for 3y^'+7y=x^3-2x^2+1 is y=(343x^3-1127x^2+966x-71}{2401}+(c_{1})/(e^{\frac{7x)/3)}