y^{''}+y=cos(-t+pi/2)

Lösung

y^{^{''}} + y = cos (- t + \frac{π}{2})

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

Schritte zur Lösung

y^{''} (t) + y = cos (- t + \frac{π}{2})

Solve linear ODE:

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

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

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

y^{^{''}} + 3 y^{^{'}} + 2 y = e^{x}

x^{^{''}} + 4 x^{^{'}} + 13 x = 5

9 y^{^{''}} - 4 y = sin (x)

\frac{d ^{2} y}{d x ^{2}} + y = cos (x)