1/4 y^{''}+4y=3tan(4t)-1/2 e^{2t}

Lösung

\frac{1}{4} y^{^{''}} + 4 y = 3 tan (4 t) - \frac{1}{2} e^{2 t}

y = c_{1} cos (4 t) + c_{2} sin (4 t) + \frac{- 15 cos ( 4 t ) ln ( sec ( 4 t ) + tan ( 4 t ) ) - 2 e ^{2 t} cos ^{2} ( 4 t ) - 2 e ^{2 t} sin ^{2} ( 4 t )}{20}

Schritte zur Lösung

\frac{1}{4} y^{''} (t) + 4 y = 3 tan (4 t) - \frac{1}{2} e^{2 t}

Solve linear ODE:

y = c_{1} cos (4 t) + c_{2} sin (4 t) + \frac{- 15 cos ( 4 t ) ln ( sec ( 4 t ) + tan ( 4 t ) ) - 2 e ^{2 t} cos ^{2} ( 4 t ) - 2 e ^{2 t} sin ^{2} ( 4 t )}{20}

y = c_{1} cos (4 t) + c_{2} sin (4 t) + \frac{- 15 cos ( 4 t ) ln ( sec ( 4 t ) + tan ( 4 t ) ) - 2 e ^{2 t} cos ^{2} ( 4 t ) - 2 e ^{2 t} sin ^{2} ( 4 t )}{20}

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

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

y^{^{''}} + 8 y^{^{'}} + 17 y = 2 e^{- 3 x}

x^{^{''}} + 2 x^{^{'}} + 41 x = 8 cos (6 t)

y^{^{'''}} + 64 y^{^{'}} = tan (8 x)