y^{''}+9y=x^2e^{3x}+6

Lösung

y^{^{''}} + 9 y = x^{2} e^{3 x} + 6

y = c_{1} cos (3 x) + c_{2} sin (3 x) + \frac{e ^{3 x} x ^{2}}{18} - \frac{e ^{3 x} x}{27} + \frac{1}{162} e^{3 x} + \frac{2}{3}

Schritte zur Lösung

y^{''} (x) + 9 y = x^{2} e^{3 x} + 6

Solve linear ODE:

y = c_{1} cos (3 x) + c_{2} sin (3 x) + \frac{e ^{3 x} x ^{2}}{18} - \frac{e ^{3 x} x}{27} + \frac{1}{162} e^{3 x} + \frac{2}{3}

y = c_{1} cos (3 x) + c_{2} sin (3 x) + \frac{e ^{3 x} x ^{2}}{18} - \frac{e ^{3 x} x}{27} + \frac{1}{162} e^{3 x} + \frac{2}{3}

y^{^{''}} - y^{^{'}} - 2 y = 4 x^{2}, y (0) = 1, y^{^{'}} (0) = 4

y^{^{''}} - 2 y^{^{'}} - 3 y = 4 e x - 12

4 y^{^{''}} + 4 y^{^{'}} + y = e^{\frac{- x}{2}}

y^{^{''}} + 4 y^{^{'}} + 5 y = - 15 x + e^{- x}

4 y^{^{''}} - 4 y^{^{'}} + y = 24 e^{\frac{t}{2}}