(d^2+3d+1)y=x^2e^{3x}

Lösung

(d^{2} + 3 d + 1) \cdot y = x^{2} \cdot e^{3 x}

y = c_{1} e^{\frac{( - 3 + 5 ) x}{2}} + c_{2} e^{\frac{( - 3 - 5 ) x}{2}} + \frac{e ^{3 x} x ^{2}}{19} - \frac{18 e ^{3 x} x}{361} + \frac{124}{6859} e^{3 x}

Schritte zur Lösung

(d^{2} + 3 d + 1) y = x^{2} e^{3 x}

Solve linear ODE:

y = c_{1} e^{\frac{( - 3 + 5 ) x}{2}} + c_{2} e^{\frac{( - 3 - 5 ) x}{2}} + \frac{e ^{3 x} x ^{2}}{19} - \frac{18 e ^{3 x} x}{361} + \frac{124}{6859} e^{3 x}

y = c_{1} e^{\frac{( - 3 + 5 ) x}{2}} + c_{2} e^{\frac{( - 3 - 5 ) x}{2}} + \frac{e ^{3 x} x ^{2}}{19} - \frac{18 e ^{3 x} x}{361} + \frac{124}{6859} e^{3 x}

(d^{2} + 4) y = x^{2}

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

(d^{2} - 1) y = e^{x}

4 y^{^{''}} + 4 y^{^{'}} + 3 y = 4 e^{- 3} x + 18 x + 15

(d^{5} - d) y = 12 e^{x} + 8 sin (x) - 2 x