1/8 y^{''}+4y^'+28x=0,y(0)=0,y^'(0)=3

Lösung

\frac{1}{8} y^{^{''}} + 4 y^{^{'}} + 28 x = 0, y (0) = 0, y^{^{'}} (0) = 3

y = \frac{89}{1024} - \frac{89}{1024} e^{- 32 x} - \frac{7 x ^{2}}{2} + \frac{7 x}{32}

Schritte zur Lösung

\frac{1}{8} y^{''} (x) + 4 y^{'} (x) + 28 x = 0

Solve linear ODE:

y = \frac{89}{1024} - \frac{89}{1024} e^{- 32 x} - \frac{7 x ^{2}}{2} + \frac{7 x}{32}

y = \frac{89}{1024} - \frac{89}{1024} e^{- 32 x} - \frac{7 x ^{2}}{2} + \frac{7 x}{32}

- 6 y^{^{''}} - 5 y^{^{'}} - y = - (t^{2} + 2 t + 2 e^{2 t})

0.75 y^{^{''}} + 50 y = 5 t^{2}

(D^{2} - 5 D + 6) y = x^{2} e^{3 x}

y^{^{''}} + 10 y^{^{'}} + 20 y = 50 sinh (5 x)

\frac{d ^{4} y}{d x ^{4}} + 3 \frac{d ^{2} y}{d x ^{2}} - 4 = 0