y^{'''}+265y^'=tan(16x)

Lösung

y^{^{'''}} + 265 y^{^{'}} = tan (16 x)

y = c_{1} + c_{2} cos (265 x) + c_{3} sin (265 x) - \frac{1}{4240} ln (cos (16 x)) + cos (265 x) \cdot \int - \frac{cos ( 265 x ) tan ( 16 x )}{265} d x + sin (265 x) \cdot \int - \frac{sin ( 265 x ) tan ( 16 x )}{265} d x

Schritte zur Lösung

y^{'''} (x) + 265 y^{'} (x) = tan (16 x)

Solve linear ODE:

y = c_{1} + c_{2} cos (265 x) + c_{3} sin (265 x) - \frac{1}{4240} ln (cos (16 x)) + cos (265 x) \cdot \int - \frac{cos ( 265 x ) tan ( 16 x )}{265} d x + sin (265 x) \cdot \int - \frac{sin ( 265 x ) tan ( 16 x )}{265} d x

y = c_{1} + c_{2} cos (265 x) + c_{3} sin (265 x) - \frac{1}{4240} ln (cos (16 x)) + cos (265 x) \cdot \int - \frac{cos ( 265 x ) tan ( 16 x )}{265} d x + sin (265 x) \cdot \int - \frac{sin ( 265 x ) tan ( 16 x )}{265} d x

y^{^{''}} - 10 y^{^{'}} + 9 y = e^{2 x}

y^{^{''}} + y^{^{'}} - 6 y = e^{2 t} + t

y^{^{'''}} - 3 y^{^{''}} - y^{^{'}} + 3 y = 1 + e^{x}

y^{^{''}} - y = 2 e^{- t}, y (0) = 0, y^{^{'}} (0) = 0

2 y^{^{''}} + 3 y^{^{'}} - 2 y = 10 x^{2} - 4 x - 15