(D^4+10D^2+9)y=sin(3x)+cos(3x)

Lösung

(D^{4} + 10 D^{2} + 9) y = sin (3 x) + cos (3 x)

y = c_{1} cos (x) + c_{2} sin (x) + c_{3} cos (3 x) + c_{4} sin (3 x) - \frac{x sin ( 3 x )}{48} + \frac{x cos ( 3 x )}{48}

Schritte zur Lösung

(D^{4} + 10 D^{2} + 9) y = sin (3 x) + cos (3 x)

Solve linear ODE:

y = c_{1} cos (x) + c_{2} sin (x) + c_{3} cos (3 x) + c_{4} sin (3 x) - \frac{x sin ( 3 x )}{48} + \frac{x cos ( 3 x )}{48}

y = c_{1} cos (x) + c_{2} sin (x) + c_{3} cos (3 x) + c_{4} sin (3 x) - \frac{x sin ( 3 x )}{48} + \frac{x cos ( 3 x )}{48}

y^{^{''}} + 36 y = 2 e^{6 x}

y^{^{''}} + 2 y^{^{'}} - 8 y = 2 e^{4 t}

d (x) = \frac{3}{2 x}

(d^{2} + 6 d + 9) y = \frac{e ^{- 3} x}{x ^{3}}

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