(d^2y)/(dx^2)-4(dy)/(dx)+4y=3x-4

Lösung

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

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

Schritte zur Lösung

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

Solve linear ODE:

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

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

\frac{d ^{2} x}{d t ^{2}} + 9 x = e^{t} + sin (t)

y^{^{''}} - 4 y^{^{'}} + 4 y = t^{2} e^{2 t} + e^{2 t}

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

\frac{d ^{2} y}{d x ^{2}} - 6 \frac{d y}{d x} + 9 y = 2 sin (4 x)

y^{^{''}} + 5 y = 6 t^{2} - 9, y (0) = 0, y^{^{'}} (0) = - 3