y^{''}+9y=cos(t)*\H(t-pi)

Lösung

y^{^{''}} + 9 y = cos (t) \cdot H (t - π)

y = c_{1} cos (3 t) + c_{2} sin (3 t) + cos (3 t) \cdot \int - \frac{sin ( 3 t ) cos ( t ) H ( t - π )}{3} d t + sin (3 t) \cdot \int \frac{cos ( 3 t ) cos ( t ) H ( t - π )}{3} d t

Schritte zur Lösung

y^{''} (t) + 9 y = cos (t) \cdot H (t - π)

Solve linear ODE:

y = c_{1} cos (3 t) + c_{2} sin (3 t) + cos (3 t) \cdot \int - \frac{sin ( 3 t ) cos ( t ) H ( t - π )}{3} d t + sin (3 t) \cdot \int \frac{cos ( 3 t ) cos ( t ) H ( t - π )}{3} d t

y = c_{1} cos (3 t) + c_{2} sin (3 t) + cos (3 t) \cdot \int - \frac{sin ( 3 t ) cos ( t ) H ( t - π )}{3} d t + sin (3 t) \cdot \int \frac{cos ( 3 t ) cos ( t ) H ( t - π )}{3} d t

y^{^{''}} - 4 y^{^{'}} + 3 y = 2 e^{3 x}

so l v e f or D, D (x) = \frac{45}{x + 3}

y^{^{''}} - y^{^{'}} = t

y^{^{''}} + y = x^{2} + x - 1

(D^{3} - 3 D^{2} + 4 D - 2) y = cos (x)