y^{''}+4y=t^2+6e^t

Lösung

y^{^{''}} + 4 y = t^{2} + 6 e^{t}

y = c_{1} cos (2 t) + c_{2} sin (2 t) + \frac{t ^{2}}{4} - \frac{1}{8} + \frac{6}{5} e^{t}

Schritte zur Lösung

y^{''} (t) + 4 y = t^{2} + 6 e^{t}

Solve linear ODE:

y = c_{1} cos (2 t) + c_{2} sin (2 t) + \frac{t ^{2}}{4} - \frac{1}{8} + \frac{6}{5} e^{t}

y = c_{1} cos (2 t) + c_{2} sin (2 t) + \frac{t ^{2}}{4} - \frac{1}{8} + \frac{6}{5} e^{t}

y^{^{''}} - 2 y^{^{'}} + 5 y = 10 x^{2} - 3 x - 3

y^{^{''}} + 4 y = 3 cos (x)

y^{^{''}} - 8 y^{^{'}} + 4 y = x e^{x}

y^{^{''}} + 4 y = 8 tan (t)

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