y^{''''}+9y^{''}=sin(3t)+te^{4t}+4

Lösung

y^{^{''''}} + 9 y^{^{''}} = sin (3 t) + t e^{4 t} + 4

y = c_{1} + c_{2} t + c_{3} cos (3 t) + c_{4} sin (3 t) + \frac{t cos ( 3 t )}{54} + \frac{e ^{4 t} t}{400} - \frac{41}{20000} e^{4 t} + \frac{2 t ^{2}}{9}

Schritte zur Lösung

y^{(4)} (t) + 9 y^{''} (t) = sin (3 t) + t e^{4 t} + 4

Solve linear ODE:

y = c_{1} + c_{2} t + c_{3} cos (3 t) + c_{4} sin (3 t) + \frac{t cos ( 3 t )}{54} + \frac{e ^{4 t} t}{400} - \frac{41}{20000} e^{4 t} + \frac{2 t ^{2}}{9}

y = c_{1} + c_{2} t + c_{3} cos (3 t) + c_{4} sin (3 t) + \frac{t cos ( 3 t )}{54} + \frac{e ^{4 t} t}{400} - \frac{41}{20000} e^{4 t} + \frac{2 t ^{2}}{9}

\frac{d ^{2} y}{d x ^{2}} - \frac{d y}{d x} - 2 y = 4 x^{2}

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

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

y^{^{''}} + 8 y^{^{'}} + 16 y = 2 sin (4 x)

y^{^{''}} + 4 y^{^{'}} + 4 = \frac{1}{x ^{2} e ^{2 x}}