y^{''}+3y^'-5y=(4x^2-7x+0)e^{4x}

Lösung

y^{^{''}} + 3 y^{^{'}} - 5 y = (4 x^{2} - 7 x + 0) e^{4 x}

y = c_{1} e^{\frac{( - 3 + 29 ) x}{2}} + c_{2} e^{\frac{( - 3 - 29 ) x}{2}} + \frac{4 e ^{4 x} x ^{2}}{23} - \frac{249 e ^{4 x} x}{529} + \frac{2555}{12167} e^{4 x}

Schritte zur Lösung

y^{''} (x) + 3 y^{'} (x) - 5 y = (4 x^{2} - 7 x + 0) e^{4 x}

Solve linear ODE:

y = c_{1} e^{\frac{( - 3 + 29 ) x}{2}} + c_{2} e^{\frac{( - 3 - 29 ) x}{2}} + \frac{4 e ^{4 x} x ^{2}}{23} - \frac{249 e ^{4 x} x}{529} + \frac{2555}{12167} e^{4 x}

y = c_{1} e^{\frac{( - 3 + 29 ) x}{2}} + c_{2} e^{\frac{( - 3 - 29 ) x}{2}} + \frac{4 e ^{4 x} x ^{2}}{23} - \frac{249 e ^{4 x} x}{529} + \frac{2555}{12167} e^{4 x}

y^{^{''}} - 2 y^{^{'}} + y = 4 x^{2} - 6

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

y^{^{''}} + 3 y = e^{t}

y^{^{''}} - 9 y^{^{'}} = 9 x e^{- 3 x}

y^{^{''}} + 14 y^{^{'}} + 49 y = t - 2 e - 7 t