y^{''}+4y=sec(22x)

Lösung

y^{^{''}} + 4 y = sec (22 x)

y = c_{1} cos (2 x) + c_{2} sin (2 x) + cos (2 x) \cdot \int - \frac{sin ( 2 x ) sec ( 22 x )}{2} d x + sin (2 x) \cdot \int \frac{cos ( 2 x ) sec ( 22 x )}{2} d x

Schritte zur Lösung

y^{''} (x) + 4 y = sec (22 x)

Solve linear ODE:

y = c_{1} cos (2 x) + c_{2} sin (2 x) + cos (2 x) \cdot \int - \frac{sin ( 2 x ) sec ( 22 x )}{2} d x + sin (2 x) \cdot \int \frac{cos ( 2 x ) sec ( 22 x )}{2} d x

y = c_{1} cos (2 x) + c_{2} sin (2 x) + cos (2 x) \cdot \int - \frac{sin ( 2 x ) sec ( 22 x )}{2} d x + sin (2 x) \cdot \int \frac{cos ( 2 x ) sec ( 22 x )}{2} d x

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

y^{^{''}} - 2 y^{^{'}} - 3 y = 2 e^{5 t}

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

y^{^{''}} + y = cos (x - \frac{π}{2}), y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} - 3 y^{^{'}} + 2 y = e^{3} x cos (e^{x})