y^{''}+2y=sec(x)

Lösung

y^{^{''}} + 2 y = sec (x)

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

Schritte zur Lösung

y^{''} (x) + 2 y = sec (x)

Solve linear ODE:

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

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

y^{^{''}} + 3 y^{^{'}} - 54 y = - 174 t + 108 t^{2}

2 y^{^{''}} + 5 y^{^{'}} + 3 y = \frac{1}{4} ln (x + 1)

y^{^{''}} + 9 y = 17 sec^{2} (3 t)

y^{^{''}} + 4 y^{^{'}} + 8 y = 8 x^{2} + 8 x + 1

y^{^{''''}} + 2 y^{^{''}} + 1 = 7 sin (t)