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

解

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}}}

解答ステップ

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

線形 ODE を解く:

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}}}