6y^{''}-y^'-2y=3sin(10)x

Lösung

6 y^{^{''}} - y^{^{'}} - 2 y = 3 sin (10) x

y = c_{1} e^{\frac{2 x}{3}} + c_{2} e^{- \frac{x}{2}} - \frac{3 sin ( 10 ) x}{2} + \frac{3 sin ( 10 )}{4}

Schritte zur Lösung

6 y^{''} (x) - y^{'} (x) - 2 y = 3 sin (10) x

Solve linear ODE:

y = c_{1} e^{\frac{2 x}{3}} + c_{2} e^{- \frac{x}{2}} - \frac{3 sin ( 10 ) x}{2} + \frac{3 sin ( 10 )}{4}

y = c_{1} e^{\frac{2 x}{3}} + c_{2} e^{- \frac{x}{2}} - \frac{3 sin ( 10 ) x}{2} + \frac{3 sin ( 10 )}{4}

so l v e f or d, d (x) = \frac{3 x - 2}{x + 1}

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

\frac{d ^{2} y}{d x ^{2}} - 6 \frac{d y}{d x} = 37 sin (x)

y^{^{''}} - 7 y^{^{'}} + 10 y = e^{x}

y^{^{''}} + k y = g - 6 t, y (0) = 0, y^{^{'}} (0) = 0