(d^2x)/(dt^2)-3(dx)/(dt)+12x=9t

Lösung

\frac{d ^{2} x}{d t ^{2}} - 3 \frac{d x}{d t} + 12 x = 9 t

x = e^{\frac{3 t}{2}} (c_{1} cos (\frac{39 t}{2}) + c_{2} sin (\frac{39 t}{2})) + \frac{3 t}{4} + \frac{3}{16}

Schritte zur Lösung

\frac{d ^{2} x}{d t ^{2}} - 3 \frac{d x}{d t} + 12 x = 9 t

Solve linear ODE:

x = e^{\frac{3 t}{2}} (c_{1} cos (\frac{39 t}{2}) + c_{2} sin (\frac{39 t}{2})) + \frac{3 t}{4} + \frac{3}{16}

x = e^{\frac{3 t}{2}} (c_{1} cos (\frac{39 t}{2}) + c_{2} sin (\frac{39 t}{2})) + \frac{3 t}{4} + \frac{3}{16}

y^{^{''}} + y^{^{'}} + 5 y = 2 x

y^{^{''}} - 4 y^{^{'}} + 13 y = e^{2 t} \cdot sin (3 t), y (0) = 4

y^{^{''}} + y^{^{'}} = e^{x} + 3 x

l in e a r y^{^{''}} + 4 y = x^{2} + 5 cos (x)

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