y^{''}+4y^'+7t=t^3e^{4t}cos(t)

Lösung

y^{^{''}} + 4 y^{^{'}} + 7 t = t^{3} e^{4 t} cos (t)

y = c_{1} + c_{2} e^{- 4 t} + \int \frac{e ^{4 t} t ^{3} cos ( t ) - 7 t}{4} d t + e^{- 4 t} \cdot \int - \frac{e ^{4 t} t ^{3} cos ( t ) - 7 t}{4 e ^{- 4 t}} d t

Schritte zur Lösung

y^{''} (t) + 4 y^{'} (t) + 7 t = t^{3} e^{4 t} cos (t)

Solve linear ODE:

y = c_{1} + c_{2} e^{- 4 t} + \int \frac{e ^{4 t} t ^{3} cos ( t ) - 7 t}{4} d t + e^{- 4 t} \cdot \int - \frac{e ^{4 t} t ^{3} cos ( t ) - 7 t}{4 e ^{- 4 t}} d t

y = c_{1} + c_{2} e^{- 4 t} + \int \frac{e ^{4 t} t ^{3} cos ( t ) - 7 t}{4} d t + e^{- 4 t} \cdot \int - \frac{e ^{4 t} t ^{3} cos ( t ) - 7 t}{4 e ^{- 4 t}} d t

\frac{d ^{2} y}{d x ^{2}} - y = sin^{2} (x)

y^{^{''}} - 2 y^{^{'}} + 26 y = e x cos (5 x)

y^{^{''}} - 2 y^{^{'}} - 3 y = \frac{12 e ^{4 x}}{1 + e ^{2 x}}

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

y^{^{''}} - 2 y^{^{'}} = 5 t^{4}, y (0) = 1, y^{^{'}} (0) = 0