y^{''}-y^'+y=(sin(t))/3-2e^{2t}

Lösung

y^{^{''}} - y^{^{'}} + y = \frac{sin ( t )}{3} - 2 e^{2 t}

y = e^{\frac{t}{2}} (c_{1} cos (\frac{3 t}{2}) + c_{2} sin (\frac{3 t}{2})) + \frac{cos ( t ) - 2 e ^{2 t}}{3}

Schritte zur Lösung

y^{''} (t) - y^{'} (t) + y = \frac{sin ( t )}{3} - 2 e^{2 t}

Solve linear ODE:

y = e^{\frac{t}{2}} (c_{1} cos (\frac{3 t}{2}) + c_{2} sin (\frac{3 t}{2})) + \frac{cos ( t ) - 2 e ^{2 t}}{3}

y = e^{\frac{t}{2}} (c_{1} cos (\frac{3 t}{2}) + c_{2} sin (\frac{3 t}{2})) + \frac{cos ( t ) - 2 e ^{2 t}}{3}

x^{^{''}} + 3 x^{^{'}} + 2 x = cos (2 t)

y^{^{''}} + 4 y = 10 e^{5 x}

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

y^{^{'''}} - y^{^{''}} + y^{^{'}} - y = sec (t)

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