y^{''}+y+y=((e^t))/t

Lösung

y^{^{''}} + y + y = \frac{( e ^{t} )}{t}

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

Schritte zur Lösung

y^{''} (t) + y + y = \frac{( e ^{t} )}{t}

Solve linear ODE:

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

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

y^{^{''}} - 4 y^{^{'}} + 3 y = 13 cos (2 x)

y^{^{'''}} - 6 y^{^{''}} + 12 y^{^{'}} - 8 y = t e^{3} + 1

y^{^{''}} + y^{^{'}} - 2 y = 2 (3 x + 1) e^{x} + 20 cos (2 x)

y^{^{''}} + 12 y = 8 e^{4 x}

y^{^{''}} + 2 y^{^{'}} + y = \frac{t}{e ^{t}}