(d^2y)/(dt^2)-5(dy)/(dt)+5y=1+t

Lösung

\frac{d ^{2} y}{d t ^{2}} - 5 \frac{d y}{d t} + 5 y = 1 + t

y = c_{1} e^{\frac{( 5 + 5 ) t}{2}} + c_{2} e^{\frac{( 5 - 5 ) t}{2}} + \frac{t}{5} + \frac{2}{5}

Schritte zur Lösung

\frac{d ^{2} y}{d t ^{2}} - 5 \frac{d y}{d t} + 5 y = 1 + t

Solve linear ODE:

y = c_{1} e^{\frac{( 5 + 5 ) t}{2}} + c_{2} e^{\frac{( 5 - 5 ) t}{2}} + \frac{t}{5} + \frac{2}{5}

y = c_{1} e^{\frac{( 5 + 5 ) t}{2}} + c_{2} e^{\frac{( 5 - 5 ) t}{2}} + \frac{t}{5} + \frac{2}{5}

y^{^{''}} + 4 y^{^{'}} + 20 y = 4 cos (2 x)

7 y^{^{''}} + 5 y^{^{'}} - y = 9

y^{^{''}} + 3 y^{^{'}} + 2.25 y = 9 t^{3} + 64, y (0) = 1, y^{^{'}} (0) = 31.5

y^{^{''}} + 3 y^{^{'}} - 4 y = - 32 t^{2}

y^{^{''}} + y^{^{'}} = (2 t)